@standard{1998a,
  title = {Guide for the Verification and Validation of Computational Fluid Dynamics Simulations},
  year = {1998},
  publisher = {{American Institute of Aeronautics and Astronautics, Inc.}},
}

@book{2005,
  title = {Algorithmic {{Learning}} in a {{Random World}}},
  year = {2005},
  publisher = {Springer-Verlag},
  address = {New York},
  urldate = {2024-01-10},
  langid = {english},
  keywords = {algorithms,Approximation,classification,Conformal prediction,learning,machine learning,modeling,Randomness,Regression},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Conformal Prediction\Algorithmic_Learning_in_a_Random_World_2005.pdf}
}

@techreport{2008,
  type = {Guide},
  title = {Evaluation of Measurement Data --- {{Guide}} to the Expression of Uncertainty in Measurements.Pdf},
  year = {2008},
  pages = {134},
  institution = {JCGM},
  langid = {english},
  keywords = {Examples,Experiments,Measurements,Uncertainty,Uncertainty Quantification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Uncertainty Quantification\Evaluation_of_measurement_data_—_Guide_to_the_expression_of_uncertainty_in_2008.pdf}
}

@article{2023,
  title = {A New Active-Learning Estimation Method for the Failure Probability of Structural Reliability Based on {{Kriging}} Model and Simple Penalty Function},
  year = {2023},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {410},
  pages = {116035},
  publisher = {North-Holland},
  urldate = {2023-12-01},
  abstract = {Since the Kriging model can provide the mean value of the performance function at a sample point and the corresponding variance among the various surr{\dots}},
  langid = {american},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Reliability Analysis\A_new_active-learning_estimation_method_for_the_failure_probability_of_2023.pdf}
}

@misc{abadi2015,
  title = {\{\vphantom\}{{TensorFlow}}\vphantom\{\}: {{Large-Scale Machine Learning}} on {{Heterogeneous Systems}}},
	author = {Abadi, Mart{\'i}n and Agarwal, Ashish and {Paul Barham} and {Eugene Brevdo} and {Zhifeng Chen} and others},
  year = {2015}
}

@book{abramowitz1972,
  title = {Handbook of {{Mathematical Functions}}: With {{Formulas}}, {{Graphs}}, and {{Mathematical Tables}}},
  shorttitle = {Handbook of {{Mathematical Functions}}},
  year = {1972},
  series = {Applied {{Mathematics}}},
  edition = {10},
  number = {55},
  publisher = {National Bureau of Standards},
  langid = {english}
}

@book{ackley1987,
  title = {A Connectionist Machine for Genetic Hillclimbing},
	author = {Ackley, David H.},
  year = {1987},
  series = {The {{Kluwer}} International Series in Engineering and Computer Science},
  number = {SECS 28},
  publisher = {Kluwer Academic Publishers},
  address = {Boston},
  lccn = {Q336 .A25 1987},
  keywords = {Artificial intelligence,Connectionism,Data processing}
}

@book{AIAA1998,
  title = {Guide: {{Guide}} for the {{Verification}} and {{Validation}} of {{Computational Fluid Dynamics Simulations}} ({{AIAA G-077-1998}}(2002))},
  shorttitle = {Guide},
  year = {1998},
  publisher = {{American Institute of Aeronautics and Astronautics, Inc.}},
  address = {Washington, DC},
  urldate = {2021-09-07},
  langid = {english},
  keywords = {Guideline,Model Validation},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Norm, Standard & Guidelines\Computational_Fluid_Dynamics_Committee-Guide_1998.pdf}
}

@article{ajdari2014,
  title = {An {{Adaptive Exploration-Exploitation Algorithm}} for {{Constructing Metamodels}} in {{Random Simulation Using}} a {{Novel Sequential Experimental Design}}},
	author = {Ajdari, Ali and Mahlooji, Hashem},
  year = {2014},
  journal = {Communications in Statistics - Simulation and Computation},
  volume = {43},
  number = {5},
  pages = {947--968},
  urldate = {2022-03-28},
  langid = {english}
}

@article{akiba2019,
  title = {Optuna: {{A Next-generation Hyperparameter Optimization Framework}}},
  shorttitle = {Optuna},
	author = {Akiba, Takuya and Sano, Shotaro and Yanase, Toshihiko and Ohta, Takeru and Koyama, Masanori},
  year = {2019},
  journal = {arXiv:1907.10902},
  eprint = {1907.10902},
  urldate = {2022-04-03},
  abstract = {The purpose of this study is to introduce new design-criteria for next-generation hyperparameter optimization software. The criteria we propose include (1) define-by-run API that allows users to construct the parameter search space dynamically, (2) efficient implementation of both searching and pruning strategies, and (3) easy-to-setup, versatile architecture that can be deployed for various purposes, ranging from scalable distributed computing to light-weight experiment conducted via interactive interface. In order to prove our point, we will introduce Optuna, an optimization software which is a culmination of our effort in the development of a next generation optimization software. As an optimization software designed with define-by-run principle, Optuna is particularly the first of its kind. We will present the design-techniques that became necessary in the development of the software that meets the above criteria, and demonstrate the power of our new design through experimental results and real world applications. Our software is available under the MIT license (https://github.com/pfnet/optuna/).},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Software_Packages\\Akiba_et_al-Optuna_2019.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\W88LSVBY\\1907.html}
}

@inproceedings{alaa2020,
  title = {Discriminative {{Jackknife}}: {{Quantifying Uncertainty}} in {{Deep Learning}} via {{Higher-Order Influence Functions}}},
  shorttitle = {Discriminative {{Jackknife}}},
  booktitle = {Proceedings of the 37th {{International Conference}} on {{Machine Learning}}},
	author = {Alaa, Ahmed and Schaar, Mihaela Van Der},
  year = {2020},
  pages = {165--174},
  publisher = {PMLR},
  urldate = {2024-01-10},
  abstract = {Deep learning models achieve high predictive accuracy across a broad spectrum of tasks, but rigorously quantifying their predictive uncertainty remains challenging. Usable estimates of predictive uncertainty should (1) cover the true prediction targets with high probability, and (2) discriminate between high- and low confidence prediction instances. Existing methods for uncertainty quantification are based predominantly on Bayesian neural networks; these may fall short of (1) and (2) \{---\} i.e., Bayesian credible intervals do not guarantee frequentist coverage, and approximate posterior inference undermines discriminative accuracy. In this paper, we develop the discriminative jackknife (DJ), a frequentist procedure that utilizes influence functions of a model's loss functional to construct a jackknife (or leave one-out) estimator of predictive confidence intervals. The DJ satisfies (1) and (2), is applicable to a wide range of deep learning models, is easy to implement, and can be applied in a post-hoc fashion without interfering with model training or compromising its accuracy. Experiments demonstrate that DJ performs competitively compared to existing Bayesian and non-Bayesian regression baselines.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Conformal Prediction\Alaa_Schaar-Discriminative_Jackknife_2020.pdf}
}

@misc{ameli2022,
  title = {Noise {{Estimation}} in {{Gaussian Process Regression}}},
	author = {Ameli, Siavash and Shadden, Shawn C.},
  year = {2022},
  number = {arXiv:2206.09976},
  eprint = {2206.09976},
  primaryclass = {cs, math, stat},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the correlated error, and the variance of the noise based on maximizing a marginal likelihood function. Our method involves suitably reducing the dimensionality of the hyperparameter space to simplify the estimation procedure to a univariate root-finding problem. Moreover, we derive bounds and asymptotes of the marginal likelihood function and its derivatives, which are useful to narrowing the initial range of the hyperparameter search. Using numerical examples, we demonstrate the computational advantages and robustness of the presented approach compared to traditional parameter optimization.},
  archiveprefix = {arxiv},
  keywords = {62J05 62H12,Computer Science - Machine Learning,Mathematics - Optimization and Control,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Ameli_Shadden-Noise_Estimation_in_Gaussian_Process_Regression_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\4Y3WRNC4\\2206.html}
}

@inproceedings{amos2017,
  title = {Input {{Convex Neural Networks}}},
  booktitle = {Proceedings of the 34th {{International Conference}} on {{Machine Learning}}},
	author = {Amos, Brandon and Xu, Lei and Kolter, J. Zico},
  year = {2017},
  pages = {146--155},
  publisher = {PMLR},
  urldate = {2023-05-18},
  abstract = {This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of) the inputs. The networks allow for efficient inference via optimization over some inputs to the network given others, and can be applied to settings including structured prediction, data imputation, reinforcement learning, and others. In this paper we lay the basic groundwork for these models, proposing methods for inference, optimization and learning, and analyze their representational power. We show that many existing neural network architectures can be made input-convex with a minor modification, and develop specialized optimization algorithms tailored to this setting. Finally, we highlight the performance of the methods on multi-label prediction, image completion, and reinforcement learning problems, where we show improvement over the existing state of the art in many cases.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Neural Networks\Amos_et_al-Input_Convex_Neural_Networks_2017.pdf}
}

@misc{angelopoulos2022,
  title = {A {{Gentle Introduction}} to {{Conformal Prediction}} and {{Distribution-Free Uncertainty Quantification}}},
	author = {Angelopoulos, Anastasios N. and Bates, Stephen},
  year = {2022},
  number = {arXiv:2107.07511},
  eprint = {2107.07511},
  primaryclass = {cs, math, stat},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {Black-box machine learning models are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Conformal prediction is a user-friendly paradigm for creating statistically rigorous uncertainty sets/intervals for the predictions of such models. Critically, the sets are valid in a distribution-free sense: they possess explicit, non-asymptotic guarantees even without distributional assumptions or model assumptions. One can use conformal prediction with any pre-trained model, such as a neural network, to produce sets that are guaranteed to contain the ground truth with a user-specified probability, such as 90\%. It is easy-to-understand, easy-to-use, and general, applying naturally to problems arising in the fields of computer vision, natural language processing, deep reinforcement learning, and so on. This hands-on introduction is aimed to provide the reader a working understanding of conformal prediction and related distribution-free uncertainty quantification techniques with one self-contained document. We lead the reader through practical theory for and examples of conformal prediction and describe its extensions to complex machine learning tasks involving structured outputs, distribution shift, time-series, outliers, models that abstain, and more. Throughout, there are many explanatory illustrations, examples, and code samples in Python. With each code sample comes a Jupyter notebook implementing the method on a real-data example; the notebooks can be accessed and easily run using our codebase.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning,Mathematics - Statistics Theory,Statistics - Machine Learning,Statistics - Methodology},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Conformal Prediction\\Angelopoulos_Bates-A_Gentle_Introduction_to_Conformal_Prediction_and_Distribution-Free_Uncertainty_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\9NIBJWGE\\2107.html}
}

@misc{antoran2022,
  title = {Adapting the {{Linearised Laplace Model Evidence}} for {{Modern Deep Learning}}},
	author = {Antor{\'a}n, Javier and Janz, David and Allingham, James Urquhart and Daxberger, Erik and Barbano, Riccardo and others},
  year = {2022},
  number = {arXiv:2206.08900},
  eprint = {2206.08900},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence, allowing for scalable selection of model hyperparameters. In this work, we examine the assumptions behind this method, particularly in conjunction with model selection. We show that these interact poorly with some now-standard tools of deep learning--stochastic approximation methods and normalisation layers--and make recommendations for how to better adapt this classic method to the modern setting. We provide theoretical support for our recommendations and validate them empirically on MLPs, classic CNNs, residual networks with and without normalisation layers, generative autoencoders and transformers.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Bayesian Neural Networks\\Antoran_et_al-Adapting_the_Linearised_Laplace_Model_Evidence_for_Modern_Deep_Learning_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\WXPRANCR\\2206.html}
}

@book{antoulas2005,
  title = {Approximation of Large-Scale Dynamical Systems},
	author = {Antoulas, Athanasios C.},
  year = {2005},
  publisher = {CAMBRIDGE},
}

@article{ao2017,
  title = {Design of Validation Experiments for Life Prediction Models},
	author = {Ao, Dan and Hu, Zhen and Mahadevan, Sankaran},
  year = {2017},
  journal = {Reliability Engineering \& System Safety},
  volume = {165},
  pages = {22--33},
  urldate = {2023-09-21},
  abstract = {This paper proposes a novel validation experiment design optimization (VEDO) method for the assurance of life prediction model, which is one of the key steps in guaranteeing the reliable design of products in meeting the target service life. Life testing data collected from experiments are important for the validation of time-dependent models. However, directly collecting life data for model validation at the operating stress level is usually time-consuming and expensive. In order to overcome this challenge, the accelerated life testing (ALT) method is employed in the proposed method to collect data for model validation. The connection between ALT and model validation is established first; then a VEDO model is developed using the prior information obtained from the computer simulation model. In the VEDO model, the information gain for model validation is maximized within the testing budget and available testing chamber constraints. The obtained optimal number of tests and testing stress levels are designed to maximize the confidence in the validation results. Various sources of uncertainty such as prediction uncertainty, uncertainty of prior information, and observation errors are included within the optimization process in order to improve the robustness of validation experiment design. A composite helicopter rotor hub component is used to demonstrate the effectiveness of the proposed VEDO method.},
  keywords = {Accelerated life testing,Experimental design,Information theory,Life prediction,Model validation},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Validation\\Efficient Model Validation\\Ao_et_al-Design_of_validation_experiments_for_life_prediction_models_2017.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\4CB3Q2IP\\S0951832016302009.html}
}

@article{arboretti2022,
  title = {Active Learning for Noisy Physical Experiments with More than Two Responses},
	author = {Arboretti, Rosa and Ceccato, Riccardo and Pegoraro, Luca and Salmaso, Luigi},
  year = {2022},
  journal = {Chemometrics and Intelligent Laboratory Systems},
  volume = {226},
  pages = {104595},
  urldate = {2023-09-18},
  abstract = {When designing experiments, one of the objectives consists in building a model for prediction of future observations. If the underlying phenomenon is complex, one option is to employ machine learning (ML) models for data analysis and to build accurate emulators that function as virtual representations of the physical process, and can be used in lieu of further evaluations of the actual physical system. However, to obtain accurate models, informative data must be provided to train the algorithms, and a typical approach consists in the sequential collection of data via active learning (AL) strategies. Most existing literature on AL focuses on computer experiments. In this paper we introduce an AL algorithm for Physical Experiments based on nonparametric Ranking and Clustering (ALPERC) that can be used for sequential data collection in noisy settings when three or more responses are investigated in the same experiment. We inspect the performance of the ALPERC algorithm through simulations and a case study application on the prediction of relevant properties of thermoelectric materials.},
  keywords = {Adaptive sampling,Batch sequential designs,Design of experiments,Interpretability,Variable importance},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\JMC6BE8K\S016974392200106X.html}
}

@article{arendt2012,
  title = {Quantification of {{Model Uncertainty}}: {{Calibration}}, {{Model Discrepancy}}, and {{Identifiability}}},
  shorttitle = {Quantification of {{Model Uncertainty}}},
	author = {Arendt, Paul D. and Apley, Daniel W. and Chen, Wei},
  year = {2012},
  journal = {Journal of Mechanical Design},
  volume = {134},
  number = {10},
  urldate = {2023-02-04},
  abstract = {To use predictive models in engineering design of physical systems, one should first quantify the model uncertainty via model updating techniques employing both simulation and experimental data. While calibration is often used to tune unknown calibration parameters of a computer model, the addition of a discrepancy function has been used to capture model discrepancy due to underlying missing physics, numerical approximations, and other inaccuracies of the computer model that would exist even if all calibration parameters are known. One of the main challenges in model updating is the difficulty in distinguishing between the effects of calibration parameters versus model discrepancy. We illustrate this identifiability problem with several examples, explain the mechanisms behind it, and attempt to shed light on when a system may or may not be identifiable. In some instances, identifiability is achievable under mild assumptions, whereas in other instances, it is virtually impossible. In a companion paper, we demonstrate that using multiple responses, each of which depends on a common set of calibration parameters, can substantially enhance identifiability.},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Validation\\Arendt_et_al-Quantification_of_Model_Uncertainty_22.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\ZWV8EUZF\\Quantification-of-Model-Uncertainty-Calibration.html}
}

@inproceedings{arendt2012a,
  title = {Improving {{Identifiability}} in {{Model Calibration Using Multiple Responses}}},
  booktitle = {{{ASME}} 2011 {{International Design Engineering Technical Conferences}} and {{Computers}} and {{Information}} in {{Engineering Conference}}},
	author = {Arendt, Paul D. and Chen, Wei and Apley, Daniel W.},
  year = {2012},
  pages = {1213--1222},
  publisher = {American Society of Mechanical Engineers Digital Collection},
  urldate = {2023-09-18},
  abstract = {The use of complex computer simulations to design, improve, optimize, or simply to better understand complex systems in many fields of science and engineering is now ubiquitous. However, simulation models are never a perfect representation of physical reality. Two general sources of uncertainty that account for the differences between simulations and experiments are parameter uncertainty and model uncertainty. The former derives from unknown model parameters, while the latter is caused by underlying missing physics, numerical approximations, and other inaccuracies of the computer simulation that exist even if all of the parameters are known. To obtain knowledge of these two sources of uncertainty, data from computer simulations (usually abundant) and data from physical experiments (typically more limited) are often combined using statistical methods. Statistical adjustment of the computer simulation model to account for the two sources of uncertainty is referred to as calibration. We argue that calibration as it is typically implemented, using only a single response variable, is challenging in that it is often extremely difficult to distinguish between the effects of parameter and model uncertainty. However, many different responses (distinct responses and/or the same response measured at different spatial and temporal locations) are automatically calculated in simulations. As multiple responses generally share a mutual dependence on the unknown parameters, they provide valuable information that can improve identifiability of parameter and model uncertainty in calibration, if they are also measured experimentally. In this paper, we explore the use of multiple responses for calibration.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\DBC\KOH\Arendt_et_al-Improving_Identifiability_in_Model_Calibration_Using_Multiple_Responses_2012.pdf}
}

@article{arridge2019,
  title = {Solving Inverse Problems Using Data-Driven Models},
	author = {Arridge, Simon and Maass, Peter and {\"O}ktem, Ozan and Sch{\"o}nlieb, Carola-Bibiane},
  year = {2019},
  journal = {Acta Numerica},
  volume = {28},
  pages = {1--174},
  publisher = {Cambridge University Press},
  urldate = {2023-02-04},
  abstract = {Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical--analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Arridge_et_al-Solving_inverse_problems_using_data-driven_models_2019.pdf}
}

@book{ASME2006,
  title = {Guide for Verification and Validation in Computational Solid Mechanics: An {{American}} National Standard},
  shorttitle = {Guide for Verification and Validation in Computational Solid Mechanics},
  year = {2006},
  series = {{{ASM V}}\&{{V}} 2006},
  number = {10},
  publisher = {ASME Press},
  address = {New York},
  langid = {english},
  keywords = {Guideline,Model Validation,Verification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Norm, Standard & Guidelines\American_Society_of_Mechanical_Engineers-Guide_for_verification_and_validation_in_computational_solid_mechanics_2006.pdf}
}

@article{aurenhammer1991,
  title = {Voronoi Diagrams---a Survey of a Fundamental Geometric Data Structure},
	author = {Aurenhammer, Franz},
  year = {1991},
  journal = {ACM Computing Surveys},
  volume = {23},
  number = {3},
  pages = {345--405},
  urldate = {2022-02-14},
  langid = {english}
}

@article{babuska2008,
  title = {Formulation of the Static Frame Problem},
	author = {Babu{\v s}ka, I. and Nobile, F. and Tempone, R.},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2496--2499},
  urldate = {2021-09-07},
  abstract = {This report describes a static framework validation challenge problem used in the SANDIA Validation Challenge Workshop, May 21--23, 2006. The challenge problem has clear engineering character, is simple to state and allows many different approaches to solve it. The regulatory assessment problem is to estimate the probability of a given vertical displacement to exceed a prescribed threshold.},
  langid = {english},
  keywords = {Examples,Model Validation,Sandia Workshop,Validation Problem},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\ValidationWS Sandia Lab\Babuska_et_al-Formulation_of_the_static_frame_problem_2008.pdf}
}

@article{babuska2008a,
  title = {Static Frame Challenge Problem: {{Summary}}},
  shorttitle = {Static Frame Challenge Problem},
	author = {Babu{\v s}ka, I. and Tempone, R.},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2572--2577},
  urldate = {2021-09-07},
  abstract = {This paper summarizes five solutions to the static frame validation challenge problem. The main goal is to highlight the different approaches present at each stage of the solution process. These include, among others, the description of the elastic properties of the frame's material and their calibration, the use of the validation and accreditation experiments for eventual model rejection and the final statement on the desired regulatory compliance, together with its reliability depending on the amount of available experimental data. It is shown that different methodologies lead to significantly different results. Finally, the conclusions highlight the main findings.},
  langid = {english},
  keywords = {Model Validation,Sandia Workshop},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\ValidationWS Sandia Lab\Babuska_Tempone-Static_frame_challenge_problem_2008.pdf}
}

@article{baker,
  title = {Stochastic {{Simulators}}: {{An Overview}} with {{Opportunities}}},
	author = {Baker, Evan and Barbillon, Pierre and Fadikar, Arindam and Gramacy, Robert B and Herbei, Radu and others},
  abstract = {In modern science, deterministic computer models are often used to understand complex phenomena, and a thriving statistical community has grown around effectively analysing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer models --- providing a catalogue of statistical methods for practitioners, an introductory view for statisticians (whether familiar with deterministic computer models or not), and an emphasis on open questions of relevance to practitioners and statisticians. Gaussian process surrogate models take center stage in this review, and these, along with several extensions needed for stochastic settings, are explained. The basic issues of designing a stochastic computer experiment and calibrating a stochastic computer model are prominent in the discussion. Instructive examples, with data and code, are used to describe the implementation and results of various methods.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Baker_et_al-Stochastic_Simulators.pdf}
}

@misc{baker2020,
  title = {Analyzing {{Stochastic Computer Models}}: {{A Review}} with {{Opportunities}}},
  shorttitle = {Analyzing {{Stochastic Computer Models}}},
	author = {Baker, Evan and Barbillon, Pierre and Fadikar, Arindam and Gramacy, Robert B. and Herbei, Radu and others},
  year = {2020},
  number = {arXiv:2002.01321},
  eprint = {2002.01321},
  primaryclass = {stat},
  publisher = {arXiv},
  abstract = {In modern science, computer models are often used to understand complex phenomena, and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer models -- providing a catalogue of statistical methods for practitioners, an introductory view for statisticians (whether familiar with deterministic computer models or not), and an emphasis on open questions of relevance to practitioners and statisticians. Gaussian process surrogate models take center stage in this review, and these, along with several extensions needed for stochastic settings, are explained. The basic issues of designing a stochastic computer experiment and calibrating a stochastic computer model are prominent in the discussion. Instructive examples, with data and code, are used to describe the implementation of, and results from, various methods.},
  archiveprefix = {arxiv},
  keywords = {Statistics - Methodology},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\Baker_et_al-Analyzing_Stochastic_Computer_Models_2020.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\FUSDNJ39\\2002.html}
}

@inproceedings{balandat2020,
  title = {{{BoTorch}}: {{A Framework}} for {{Efficient Monte-Carlo Bayesian Optimization}}},
  shorttitle = {{{BoTorch}}},
  booktitle = {Advances in {{Neural Information Processing Systems}}},
	author = {Balandat, Maximilian and Karrer, Brian and Jiang, Daniel and Daulton, Samuel and Letham, Ben and others},
  year = {2020},
  volume = {33},
  pages = {21524--21538},
  publisher = {Curran Associates, Inc.},
  urldate = {2024-01-31},
  abstract = {Bayesian optimization provides sample-efficient global optimization for a broad range of applications, including automatic machine learning, engineering, physics, and experimental design. We introduce BoTorch, a modern programming framework for Bayesian optimization that combines Monte-Carlo (MC) acquisition functions, a novel sample average approximation optimization approach, auto-differentiation, and variance reduction techniques. BoTorch's modular design facilitates flexible specification and optimization of probabilistic models written in PyTorch, simplifying implementation of new acquisition functions. Our approach is backed by novel theoretical convergence results and made practical by a distinctive algorithmic foundation that leverages fast predictive distributions, hardware acceleration, and deterministic optimization. We also propose a novel "one-shot" formulation of the Knowledge Gradient, enabled by a combination of our theoretical and software contributions. In experiments, we demonstrate the improved sample efficiency of BoTorch relative to other popular libraries.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Software_Packages\Balandat_et_al-BoTorch_2020.pdf}
}

@article{barber2021,
  title = {The Limits of Distribution-Free Conditional Predictive Inference},
	author = {Barber, Rina and Cand{\`e}s, Emmanuel J and Ramdas, Aaditya and Tibshirani, Ryan J},
  year = {2021},
  journal = {Information and Inference: A Journal of the IMA},
  volume = {10},
  number = {2},
  pages = {455--482},
  urldate = {2024-01-12},
  abstract = {We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal coverage guarantees, where predictive coverage holds on average over all possible test points, but this is not sufficient for many practical applications where we would like to know that our predictions are valid for a given individual, not merely on average over a population. On the other hand, exact conditional inference guarantees are known to be impossible without imposing assumptions on the underlying distribution. In this work, we aim to explore the space in between these two and examine what types of relaxations of the conditional coverage property would alleviate some of the practical concerns with marginal coverage guarantees while still being possible to achieve in a distribution-free setting.},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Conformal Prediction\\Foygel_Barber_et_al-The_limits_of_distribution-free_conditional_predictive_inference_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\4MTI968J\\5896927.html}
}

@article{bayarri2007,
  title = {A {{Framework}} for {{Validation}} of {{Computer Models}}},
	author = {Bayarri, Maria J and Berger, James O and Paulo, Rui and Sacks, Jerry and Cafeo, John A and others},
  year = {2007},
  journal = {Technometrics},
  volume = {49},
  number = {2},
  pages = {138--154},
  urldate = {2021-09-07},
  abstract = {In this paper, we present a framework that enables computer model evaluation oriented towards answering the question: Does the computer model adequately represent reality? The proposed validation framework is a six-step procedure based upon a mix of Bayesian statistical methodology and likelihood methodology. The methodology is particularly suited to treating the major issues associated with the validation process: quantifying multiple sources of error and uncertainty in computer models; combining multiple sources of information; and updating validation assessments as new information is acquired. Moreover, it allows inferential statements to be made about predictive error associated with model predictions in untested situations.},
  langid = {english},
  keywords = {Bayesian,Framework,Gaussian processes,Kennedy O'Hagan Framework,Model Calibration,Model Validation},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Frameworks\Bayarri_et_al-A_Framework_for_Validation_of_Computer_Models_2007.pdf}
}

@inproceedings{bayerer2008,
  title = {{{CIPS}} 2008: 5th {{International Conference}} on {{Integrated Power Electronics Systems}}, {{Proceedings}}, {{March}}, 11-13, 2008 {{Nuremberg}}/{{Germany}}},
  shorttitle = {{{CIPS}} 2008},
	author = {Bayerer, Reinhold and Herrmann, Tobias and Licht, Thomas and Lutz, Josef and Feller, Marco},
  year = {2008},
  series = {{{ETG-Fachbericht}}},
  publisher = {VDE-Verl},
  address = {Berlin Offenbach},
  langid = {english}
}

@article{bayes1763,
  title = {{LII. An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S}},
	author = {Bayes, Thomas},
  year = {1763},
  journal = {Philosophical Transactions of the Royal Society of London},
  volume = {53},
  pages = {370--418},
  urldate = {2022-01-21},
  abstract = {Dear Sir, I Now send you an essay which I have found among the papers of our deceased friend Mr. Bayes, and which, in my opinion, has great merit, and well deserves to be preserved.},
  langid = {latin},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Bayesian Inference\Bayes-LII_1763.pdf}
}

@inproceedings{bellotti2020,
  title = {Constructing Normalized Nonconformity Measures Based on Maximizing Predictive Efficiency},
  booktitle = {Proceedings of the {{Ninth Symposium}} on {{Conformal}} and {{Probabilistic Prediction}} and {{Applications}}},
	author = {Bellotti, Anthony},
  year = {2020},
  pages = {41--54},
  publisher = {PMLR},
  urldate = {2024-02-05},
  abstract = {The problem of regression in the inductive conformal prediction framework is addressed to provide prediction intervals that are optimized by predictive efficiency. A differentiable function is used to approximate the exact optimization problem of minimizing predictive inefficiency on a training data set using a conformal predictor based on a parametric normalized nonconformity measure. Gradient descent is then used to  find a solution. Since the optimization approximates the conformal predictor, this method is called surrogate conformal predictor optimization. Experiments are reported that show that it results in conformal predictors that provide improved predictive efficiency for regression problems on several data sets, whilst remaining reliable. It is also shown that the optimal parameter values typically differ for different confidence levels. Using house price data, alternative measures of  inefficiency are explored to address different application requirements.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Conformal Prediction\Bellotti-Constructing_normalized_nonconformity_measures_based_on_maximizing_predictive_2020.pdf}
}

@article{berger2019,
  title = {On the {{Statistical Formalism}} of {{Uncertainty Quantification}}},
	author = {Berger, James O. and Smith, Leonard A.},
  year = {2019},
  journal = {Annual Review of Statistics and Its Application},
  volume = {6},
  number = {1},
  pages = {433--460},
  urldate = {2023-09-18},
  abstract = {The use of models to try to better understand reality is ubiquitous. Models have proven useful in testing our current understanding of reality; for instance, climate models of the 1980s were built for science discovery, to achieve a better understanding of the general dynamics of climate systems. Scientific insights often take the form of general qualitative predictions (i.e., ``under these conditions, the Earth's poles will warm more than the rest of the planet''); such use of models differs from making quantitative forecasts of specific events (i.e. ``high winds at noon tomorrow at London's Heathrow Airport''). It is sometimes hoped that, after sufficient model development, any model can be used to make quantitative forecasts for any target system. Even if that were the case, there would always be some uncertainty in the prediction. Uncertainty quantification aims to provide a framework within which that uncertainty can be discussed and, ideally, quantified, in a manner relevant to practitioners using the forecast system. A statistical formalism has developed that claims to be able to accurately assess the uncertainty in prediction. This article is a discussion of if and when this formalism can do so. The article arose from an ongoing discussion between the authors concerning this issue, the second author generally being considerably more skeptical concerning the utility of the formalism in providing quantitative decision-relevant information.},
  keywords = {climate-like,discrepancy,emulation,forecast,insight,predictability,prediction,simulation,uncertainty,uncertainty guidance,uncertainty quantification,weather-like},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Uncertainty Quantification\Berger_Smith-On_the_Statistical_Formalism_of_Uncertainty_Quantification_2019.pdf}
}

@inproceedings{bergstra2011,
  title = {Algorithms for {{Hyper-Parameter Optimization}}},
  booktitle = {Advances in {{Neural Information Processing Systems}}},
	author = {Bergstra, James and Bardenet, R{\'e}mi and Bengio, Yoshua and K{\'e}gl, Bal{\'a}zs},
  year = {2011},
  volume = {24},
  publisher = {Curran Associates, Inc.}
}

@book{berlinet2004,
  title = {Reproducing {{Kernel Hilbert Spaces}} in {{Probability}} and {{Statistics}}},
	author = {Berlinet, Alain and {Thomas-Agnan}, Christine},
  year = {2004},
  publisher = {Springer US},
  address = {Boston, MA},
  urldate = {2023-11-19},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Berlinet_Thomas-Agnan-Reproducing_Kernel_Hilbert_Spaces_in_Probability_and_Statistics_22.pdf}
}

@book{beyer2001,
  title = {The {{Theory}} of {{Evolution Strategies}}},
	author = {Beyer, Hans-Georg},
  year = {2001},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  abstract = {Evolutionary Algorithms, in particular Evolution Strategies, Genetic Algorithms, or Evolutionary Programming, have found wide acceptance as robust optimization algorithms in the last ten years. Compared with the broad propagation and the resulting practical prosperity in different scientific fields, the theory has not progressed as much. This monograph provides the framework and the first steps toward the theoretical analysis of Evolution Strategies (ES). The main emphasis is on understanding the functioning of these probabilistic optimization algorithms in real-valued search spaces by investigating the dynamical properties of some well-established ES algorithms. The book introduces the basic concepts of this analysis, such as progress rate, quality gain, and self-adaptation response, and describes how to calculate these quantities. Based on the analysis, functioning principles are derived, aiming at a qualitative understanding of why and how ES algorithms work},
  langid = {english},
  annotation = {OCLC: 851389149}
}

@article{bialecki2005,
  title = {Proper Orthogonal Decomposition and Modal Analysis for Acceleration of Transient {{FEM}} Thermal Analysis},
	author = {Bialecki, R. A. and Kassab, A. J. and Fic, A.},
  year = {2005},
  journal = {International Journal for Numerical Methods in Engineering},
  volume = {62},
  number = {6},
  pages = {774--797},
}

@article{bichon2008,
  title = {Efficient {{Global Reliability Analysis}} for {{Nonlinear Implicit Performance Functions}}},
	author = {Bichon, B. J. and Eldred, M. S. and Swiler, L. P. and Mahadevan, S. and McFarland, J. M.},
  year = {2008},
  journal = {AIAA Journal},
  volume = {46},
  number = {10},
  urldate = {2023-11-16},
  langid = {english},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Reliability Analysis\\Bichon_et_al-Efficient_Global_Reliability_Analysis_for_Nonlinear_Implicit_Performance_2008.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\P46GNJW4\\1.html}
}

@book{biegler2010,
  title = {Large-{{Scale Inverse Problems}} and {{Quantification}} of {{Uncertainty}}},
  year = {2010},
  edition = {1},
  publisher = {Wiley},
  urldate = {2023-09-03},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Biegler_et_al-Large‐Scale_Inverse_Problems_and_Quantification_of_Uncertainty_22.pdf}
}

@article{bingham2018,
  title = {Pyro: {{Deep Universal Probabilistic Programming}}},
  shorttitle = {Pyro},
	author = {Bingham, Eli and Chen, Jonathan P. and Jankowiak, Martin and Obermeyer, Fritz and Pradhan, Neeraj and others},
  year = {2018},
  journal = {arXiv:1810.09538},
  eprint = {1810.09538},
  urldate = {2022-04-03},
  abstract = {Pyro is a probabilistic programming language built on Python as a platform for developing advanced probabilistic models in AI research. To scale to large datasets and high-dimensional models, Pyro uses stochastic variational inference algorithms and probability distributions built on top of PyTorch, a modern GPU-accelerated deep learning framework. To accommodate complex or model-specific algorithmic behavior, Pyro leverages Poutine, a library of composable building blocks for modifying the behavior of probabilistic programs.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Computer Science - Programming Languages,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Software_Packages\\Bingham_et_al-Pyro_2018.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\SSSRYPWP\\1810.html}
}

@article{binois2018,
  title = {Practical {{Heteroscedastic Gaussian Process Modeling}} for {{Large Simulation Experiments}}},
	author = {Binois, Micka{\"e}l and Gramacy, Robert B. and Ludkovski, Mike},
  year = {2018},
  journal = {Journal of Computational and Graphical Statistics},
  volume = {27},
  number = {4},
  pages = {808--821},
  urldate = {2024-02-05},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Binois_et_al-Practical_Heteroscedastic_Gaussian_Process_Modeling_for_Large_Simulation_2018.pdf}
}

@article{binois2019,
  title = {Replication or Exploration? {{Sequential}} Design for Stochastic Simulation Experiments},
  shorttitle = {Replication or Exploration?},
	author = {Binois, Mickael and Huang, Jiangeng and Gramacy, Robert B. and Ludkovski, Mike},
  year = {2019},
  journal = {Technometrics},
  volume = {61},
  number = {1},
  eprint = {1710.03206},
  primaryclass = {stat},
  pages = {7--23},
  urldate = {2022-08-19},
  abstract = {We investigate the merits of replication, and provide methods for optimal design (including replicates), with the goal of obtaining globally accurate emulation of noisy computer simulation experiments. We first show that replication can be beneficial from both design and computational perspectives, in the context of Gaussian process surrogate modeling. We then develop a lookahead based sequential design scheme that can determine if a new run should be at an existing input location (i.e., replicate) or at a new one (explore). When paired with a newly developed heteroskedastic Gaussian process model, our dynamic design scheme facilitates learning of signal and noise relationships which can vary throughout the input space. We show that it does so efficiently, on both computational and statistical grounds. In addition to illustrative synthetic examples, we demonstrate performance on two challenging real-data simulation experiments, from inventory management and epidemiology.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Statistics - Computation,Statistics - Methodology},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Binois_et_al-Replication_or_exploration_2019.pdf}
}

@article{binois2021,
  title = {{{{\textbf{hetGP}}}} : {{Heteroskedastic Gaussian Process Modeling}} and {{Sequential Design}} in {{{\emph{R}}}}},
  shorttitle = {{{{\textbf{hetGP}}}}},
	author = {Binois, Micka{\"e}l and Gramacy, Robert B.},
  year = {2021},
  journal = {Journal of Statistical Software},
  volume = {98},
  number = {13},
  urldate = {2022-08-19},
  abstract = {An increasing number of time-consuming simulators exhibit a complex noise structure that depends on the inputs. For conducting studies with limited budgets of evaluations, new surrogate methods are required in order to simultaneously model the mean and variance fields. To this end, we present the hetGP package, implementing many recent advances in Gaussian process modeling with input-dependent noise. First, we describe a simple, yet efficient, joint modeling framework that relies on replication for both speed and accuracy. Then we tackle the issue of data acquisition leveraging replication and exploration in a sequential manner for various goals, such as for obtaining a globally accurate model, for optimization, or for contour finding. Reproducible illustrations are provided throughout.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Binois_Gramacy-bhetGP-b__2021.pdf}
}

@misc{binois2022,
  title = {A Survey on High-Dimensional {{Gaussian}} Process Modeling with Application to {{Bayesian}} Optimization},
	author = {Binois, Mickael and Wycoff, Nathan},
  year = {2022},
  number = {arXiv:2111.05040},
  eprint = {2111.05040},
  primaryclass = {math},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {Bayesian Optimization, the application of Bayesian function approximation to finding optima of expensive functions, has exploded in popularity in recent years. In particular, much attention has been paid to improving its efficiency on problems with many parameters to optimize. This attention has trickled down to the workhorse of high dimensional BO, high dimensional Gaussian process regression, which is also of independent interest. The great flexibility that the Gaussian process prior implies is a boon when modeling complicated, low dimensional surfaces but simply says too little when dimension grows too large. A variety of structural model assumptions have been tested to tame high dimensions, from variable selection and additive decomposition to low dimensional embeddings and beyond. Most of these approaches in turn require modifications of the acquisition function optimization strategy as well. Here we review the defining structural model assumptions and discuss the benefits and drawbacks of these approaches in practice.},
  archiveprefix = {arxiv},
  keywords = {Mathematics - Optimization and Control},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Binois_Wycoff-A_survey_on_high-dimensional_Gaussian_process_modeling_with_application_to_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\P5DR3YFN\\2111.html}
}

@article{biscani2020,
  title = {A Parallel Global Multiobjective Framework for Optimization: Pagmo},
  shorttitle = {A Parallel Global Multiobjective Framework for Optimization},
	author = {Biscani, Francesco and Izzo, Dario},
  year = {2020},
  journal = {Journal of Open Source Software},
  volume = {5},
  number = {53},
  pages = {2338},
  urldate = {2022-02-14},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Software_Packages\Biscani_Izzo-A_parallel_global_multiobjective_framework_for_optimization_2020.pdf}
}

@book{bishop2006,
  title = {Pattern Recognition and Machine Learning},
	author = {Bishop, Christopher M.},
  year = {2006},
  series = {Information Science and Statistics},
  publisher = {Springer},
  address = {New York},
  langid = {english},
  lccn = {Q327 .B52 2006},
  keywords = {Basics,Bayesian,Bayesian Network,Classification,Gaussian processes,Machine learning,MCMC,Neuronal Network,Pattern perception,Probabilistic Machine Learning,Regression,Sampling,Statistics},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\PM4W32L6\Bishop - 2006 - Pattern recognition and machine learning.pdf}
}

@inproceedings{blau2022,
  title = {Optimizing {{Sequential Experimental Design}} with {{Deep Reinforcement Learning}}},
  booktitle = {Proceedings of the 39th {{International Conference}} on {{Machine Learning}}},
	author = {Blau, Tom and Bonilla, Edwin V. and Chades, Iadine and Dezfouli, Amir},
  year = {2022},
  pages = {2107--2128},
  publisher = {PMLR},
  urldate = {2023-07-19},
  abstract = {Bayesian approaches developed to solve the optimal design of sequential experiments are mathematically elegant but computationally challenging. Recently, techniques using amortization have been proposed to make these Bayesian approaches practical, by training a parameterized policy that proposes designs efficiently at deployment time. However, these methods may not sufficiently explore the design space, require access to a differentiable probabilistic model and can only optimize over continuous design spaces. Here, we address these limitations by showing that the problem of optimizing policies can be reduced to solving a Markov decision process (MDP). We solve the equivalent MDP with modern deep reinforcement learning techniques. Our experiments show that our approach is also computationally efficient at deployment time and exhibits state-of-the-art performance on both continuous and discrete design spaces, even when the probabilistic model is a black box.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Bayesian Experimental Design\Blau_et_al-Optimizing_Sequential_Experimental_Design_with_Deep_Reinforcement_Learning_2022.pdf}
}

@article{blei2017,
  title = {Variational {{Inference}}: {{A Review}} for {{Statisticians}}},
  shorttitle = {Variational {{Inference}}},
	author = {Blei, David M. and Kucukelbir, Alp and McAuliffe, Jon D.},
  year = {2017},
  journal = {Journal of the American Statistical Association},
  volume = {112},
  number = {518},
  eprint = {1601.00670},
  primaryclass = {cs, stat},
  pages = {859--877},
  urldate = {2023-05-01},
  abstract = {One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation involving the posterior density. In this paper, we review variational inference (VI), a method from machine learning that approximates probability densities through optimization. VI has been used in many applications and tends to be faster than classical methods, such as Markov chain Monte Carlo sampling. The idea behind VI is to first posit a family of densities and then to find the member of that family which is close to the target. Closeness is measured by Kullback-Leibler divergence. We review the ideas behind mean-field variational inference, discuss the special case of VI applied to exponential family models, present a full example with a Bayesian mixture of Gaussians, and derive a variant that uses stochastic optimization to scale up to massive data. We discuss modern research in VI and highlight important open problems. VI is powerful, but it is not yet well understood. Our hope in writing this paper is to catalyze statistical research on this class of algorithms.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Computation,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Statistics\\Bayesian Inference\\Blei_et_al-Variational_Inference_2017.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\UAXY58A5\\1601.html}
}

@incollection{bode2018,
  title = {Efficient {{Splitting}} of {{Test}} and {{Simulation Cases}} for the {{Verification}} of {{Highly Automated Driving Functions}}},
  booktitle = {Developments in {{Language Theory}}},
	author = {B{\"o}de, Eckard and B{\"u}ker, Matthias and Eberle, Ulrich and Fr{\"a}nzle, Martin and Gerwinn, Sebastian and others},
  year = {2018},
  volume = {11088},
  pages = {139--153},
  publisher = {Springer International Publishing},
  address = {Cham},
  urldate = {2021-09-10},
  abstract = {We address the question of feasibility of tests to verify highly automated driving functions by optimizing the trade-off between virtual tests for verifying safety properties and physical tests for validating the models used for such verification. We follow a quantitative approach based on a probabilistic treatment of the different quantities in question. That is, we quantify the accuracy of a model in terms of its probabilistic prediction ability. Similarly, we quantify the compliance of a system with its requirements in terms of the probability of satisfying these requirements. Depending on the costs of an individual virtual and physical test we are then able to calculate an optimal trade-off between physical and virtual tests, yet guaranteeing a probability of satisfying all requirements.},
  langid = {english},
  keywords = {Efficient Model Validation,Model Validation,Optimization},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Efficient Model Validation\Bode_et_al-Efficient_Splitting_of_Test_and_Simulation_Cases_for_the_Verification_of_Highly_2018.pdf}
}

@inproceedings{bogoclu2016,
  title = {A {{BENCHMARK OF CONTEMPORARY METAMODELING ALGORITHMS}}},
  booktitle = {Proceedings of the {{VII European Congress}} on {{Computational Methods}} in {{Applied Sciences}} and {{Engineering}} ({{ECCOMAS Congress}} 2016)},
	author = {Bogoclu, Can and Roos, Dirk},
  year = {2016},
  pages = {3344--3360},
  publisher = {{Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece}},
  address = {Crete Island, Greece},
  urldate = {2021-09-07},
  abstract = {Growing popularity of probabilistic and stochastic optimization methods in engineering applications has vastly increased the number of sampling points required to obtain a solution. Depending on the complexity of the underlying physical model, this often proves to be a computationally burdensome challenge. In order to overcome this challenge, one possible approach is to use surrogate models (metamodels), which approximate the responses of the physical model in a given variable subspace.},
  langid = {english},
  keywords = {Comparison,Gaussian processes,Kriging,Neuronal Network,Support Vector Machine,Surrogate Model},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\IMH\Bogoclu_Roos-A_BENCHMARK_OF_CONTEMPORARY_METAMODELING_ALGORITHMS_2016.pdf}
}

@article{bogoclu2018,
  title = {Reliability Analysis of Non-Linear and Multimodal Limit State Functions Using Adaptive {{Kriging}}},
	author = {Bogoclu, Can and Roos, Dirk},
  year = {2018},
  pages = {10},
  abstract = {The use of sampling based approaches causes the reliability analysis of multimodal limit state functions to be computationally burdensome. We propose a new kind of adaptive response surface method to increase efficiency.},
  langid = {english},
  keywords = {Gaussian processes,Kriging,Reliability (Engineering)},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\IMH\Bogoclu_Roos-Reliability_analysis_of_non-linear_and_multimodal_limit_state_functions_using_2018.pdf}
}

@article{bogoclu2021,
  title = {Local {{Latin Hypercube Refinement}} for {{Multi-objective Design Uncertainty Optimization}}},
	author = {Bogoclu, Can and Roos, Dirk and Nestorovi{\'c}, Tamara},
  year = {2021},
  journal = {Applied Soft Computing},
  volume = {112},
  urldate = {2021-09-07},
  abstract = {Optimizing the reliability and the robustness of a design is important but often unaffordable due to high sample requirements. Surrogate models based on statistical and machine learning methods are used to increase the sample efficiency. However, for higher dimensional or multi-modal systems, surrogate models may also require a large amount of samples to achieve good results. We propose a sequential sampling strategy for the surrogate based solution of multi-objective reliability based robust design optimization problems. Proposed local Latin hypercube refinement (LoLHR) strategy is model-agnostic and can be combined with any surrogate model because there is no free lunch but possibly a budget one. The proposed method is compared to stationary sampling as well as other proposed strategies from the literature. Gaussian process and support vector regression are both used as surrogate models. Empirical evidence is presented, showing that LoLHR achieves on average better results compared to other surrogate based strategies on the tested examples.},
  langid = {english},
  keywords = {Gaussian processes,Kriging,Latin Hypercube Sampling,Machine learning,Reliability (Engineering)},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\IMH\Bogoclu_et_al-Local_Latin_Hypercube_Refinement_for_Multi-objective_Design_Uncertainty_2021.pdf}
}

@article{box1964,
  title = {An Analysis of Transformations},
	author = {Box, G. E. P. and Cox, D. R.},
  year = {1964},
  journal = {Journal of the Royal Statistical Society. Series B (Methodological)},
  volume = {26},
  number = {2},
  eprint = {2984418},
  eprinttype = {jstor},
  pages = {211--252},
  urldate = {2024-02-08},
  abstract = {In the analysis of data it is often assumed that observations y1, y2, ..., yn are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters {\texttheta}. In this paper we make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's. Inferences about the transformation and about the parameters of the linear model are made by computing the likelihood function and the relevant posterior distribution. The contributions of normality, homoscedasticity and additivity to the transformation are separated. The relation of the present methods to earlier procedures for finding transformations is discussed. The methods are illustrated with examples.}
}

@article{branin1972,
  title = {Widely {{Convergent Method}} for {{Finding Multiple Solutions}} of {{Simultaneous Nonlinear Equations}}},
	author = {Branin, F. H.},
  year = {1972},
  journal = {IBM Journal of Research and Development},
  volume = {16},
  number = {5},
  pages = {504--522},
  urldate = {2022-01-20}
}

@article{brochu2010,
  title = {A {{Tutorial}} on {{Bayesian Optimization}} of {{Expensive Cost Functions}}, with {{Application}} to {{Active User Modeling}} and {{Hierarchical Reinforcement Learning}}},
	author = {Brochu, Eric and Cora, Vlad M. and {de Freitas}, Nando},
  year = {2010},
  journal = {arXiv:1012.2599},
  eprint = {1012.2599},
  urldate = {2021-09-07},
  abstract = {We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Adaptive Sampling,Bayesian Optimization,Design of Experiments,Gaussian processes,Machine learning,Optimization},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Brochu_et_al-A_Tutorial_on_Bayesian_Optimization_of_Expensive_Cost_Functions,_with_2010.pdf}
}

@inproceedings{bryan2005,
  title = {Active Learning for Identifying Function Threshold Boundaries},
  booktitle = {Advances in Neural Information Processing Systems},
	author = {Bryan, Brent and Nichol, Robert C. and Genovese, Christopher R and Schneider, Jeff and Miller, Christopher J. and others},
  year = {2005},
  volume = {18},
  publisher = {MIT Press}
}

@article{brynjarsdottir2014,
  title = {Learning about Physical Parameters: The Importance of Model Discrepancy},
  shorttitle = {Learning about Physical Parameters},
	author = {Brynjarsd{\'o}ttir, Jenn{\'y} and O'Hagan, Anthony},
  year = {2014},
  journal = {Inverse Problems},
  volume = {30},
  number = {11},
  pages = {114007},
  publisher = {IOP Publishing},
  urldate = {2023-02-04},
  abstract = {Science-based simulation models are widely used to predict the behavior of complex physical systems. It is also common to use observations of the physical system to solve the inverse problem, that is, to learn about the values of parameters within the model, a process which is often called calibration. The main goal of calibration is usually to improve the predictive performance of the simulator but the values of the parameters in the model may also be of intrinsic scientific interest in their own right. In order to make appropriate use of observations of the physical system it is important to recognize model discrepancy, the difference between reality and the simulator output. We illustrate through a simple example that an analysis that does not account for model discrepancy may lead to biased and over-confident parameter estimates and predictions. The challenge with incorporating model discrepancy in statistical inverse problems is being confounded with calibration parameters, which will only be resolved with meaningful priors. For our simple example, we model the model-discrepancy via a Gaussian process and demonstrate that through accounting for model discrepancy our prediction within the range of data is correct. However, only with realistic priors on the model discrepancy do we uncover the true parameter values. Through theoretical arguments we show that these findings are typical of the general problem of learning about physical parameters and the underlying physical system using science-based mechanistic models.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Brynjarsdottir_OʼHagan-Learning_about_physical_parameters_2014.pdf}
}

@article{brynjarsdottir2014a,
  title = {Learning about Physical Parameters: The Importance of Model Discrepancy},
  shorttitle = {Learning about Physical Parameters},
	author = {Brynjarsd{\'o}ttir, Jenn{\'y} and O'Hagan, Anthony},
  year = {2014},
  journal = {Inverse Problems},
  volume = {30},
  number = {11},
  pages = {114007},
  urldate = {2023-05-10},
  abstract = {Science-based simulation models are widely used to predict the behavior of complex physical systems. It is also common to use observations of the physical system to solve the inverse problem, i.e. to learn about the values of parameters within the model, a process often called calibration. The main goal of calibration is usually to improve the predictive performance of the simulator but the values of the parameters in the model may also be of intrinsic scientific interest in their own right.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\FT3EIYMX\Brynjarsdóttir and OʼHagan - 2014 - Learning about physical parameters the importance.pdf}
}

@article{brynjarsdottir2014b,
  title = {Learning about Physical Parameters: The Importance of Model Discrepancy},
  shorttitle = {Learning about Physical Parameters},
	author = {Brynjarsd{\'o}ttir, Jenn{\'y} and O'Hagan, Anthony},
  year = {2014},
  journal = {Inverse Problems},
  volume = {30},
  number = {11},
  pages = {114007},
  publisher = {IOP Publishing},
  urldate = {2023-09-18},
  abstract = {Science-based simulation models are widely used to predict the behavior of complex physical systems. It is also common to use observations of the physical system to solve the inverse problem, that is, to learn about the values of parameters within the model, a process which is often called calibration. The main goal of calibration is usually to improve the predictive performance of the simulator but the values of the parameters in the model may also be of intrinsic scientific interest in their own right. In order to make appropriate use of observations of the physical system it is important to recognize model discrepancy, the difference between reality and the simulator output. We illustrate through a simple example that an analysis that does not account for model discrepancy may lead to biased and over-confident parameter estimates and predictions. The challenge with incorporating model discrepancy in statistical inverse problems is being confounded with calibration parameters, which will only be resolved with meaningful priors. For our simple example, we model the model-discrepancy via a Gaussian process and demonstrate that through accounting for model discrepancy our prediction within the range of data is correct. However, only with realistic priors on the model discrepancy do we uncover the true parameter values. Through theoretical arguments we show that these findings are typical of the general problem of learning about physical parameters and the underlying physical system using science-based mechanistic models.},
  langid = {english}
}

@article{bucher1990,
  title = {A Fast and Efficient Response Surface Approach for Structural Reliability Problems},
	author = {Bucher, C.G. and Bourgund, U.},
  year = {1990},
  journal = {Structural Safety},
  volume = {7},
  number = {1},
  pages = {57--66},
  urldate = {2024-01-24},
  langid = {english}
}

@article{bucher1990a,
  title = {A Fast and Efficient Response Surface Approach for Structural Reliability Problems},
	author = {Bucher, C. G. and Bourgund, U.},
  year = {1990},
  journal = {Structural Safety},
  volume = {7},
  number = {1},
  pages = {57--66},
  urldate = {2024-02-07},
  abstract = {The reliability analysis of large and complex structural requires approximate techniques in order to reduce computational efforts to an acceptable level. Since it is, from an engineering point of view, desirable to make approximative assumptions at the level of the mechanical rather than the probabilistic modeling, simplifications should be carried out in the space of physically meaningful system- or loading variables. Within the context of this paper, a new adaptive interpolation scheme is suggested which enables fast and accurate representation of the system behavior by a response surface (RS). This response surface approach utilizes elementary statistical information on the basic variables (mean values and standard deviations) to increase the efficiency and accuracy. Thus the RS obtained is independent of the type of distribution or correlations among the basic variables which enables sensitivity studies with respect to these parameters without much computational effort. Subsequently, the response surface is utilized in conjunction with advanced Monte Carlo simulation techniques (importance sampling) to obtain the desired reliability estimates. Numerical examples are carried out in order to show the applicability of the suggested approach to structural systems reliability problems. The proposed method is shown to be superior both in efficiency and accuracy to existing approximate methods, i.e., the first order reliability methods.},
  keywords = {failure probability,importance sampling,Monte Carlo method,response surface method,structural reliability}
}

@article{burt2020,
  title = {Convergence of {{Sparse Variational Inference}} in {{Gaussian Processes Regression}}},
	author = {Burt, David R. and Rasmussen, Carl Edward and van der Wilk, Mark},
  year = {2020},
  journal = {Journal of Machine Learning Research},
  volume = {21},
  number = {131},
  pages = {1--63},
  urldate = {2023-06-14},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Burt_et_al-Convergence_of_Sparse_Variational_Inference_in_Gaussian_Processes_Regression_2020.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\U4VNZ58A\\RobustGP.html}
}

@article{butler2018,
  title = {Combining {{Push-Forward Measures}} and {{Bayes}}' {{Rule}} to {{Construct Consistent Solutions}} to {{Stochastic Inverse Problems}}},
	author = {Butler, T. and Jakeman, J. and Wildey, T.},
  year = {2018},
  journal = {SIAM Journal on Scientific Computing},
  volume = {40},
  number = {2},
  pages = {A984-A1011},
  publisher = {{Society for Industrial and Applied Mathematics}},
  urldate = {2023-07-28},
  abstract = {We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their uncertainty, the governing forward problem and its uncertainty, and a prior probability distribution describing uncertainty in the parameter field, find the posterior probability distribution over the parameter field. The prior must be chosen appropriately in order to guarantee well-posedness of the infinite-dimensional inverse problem and facilitate computation of the posterior. Furthermore, straightforward discretizations may not lead to convergent approximations of the infinite-dimensional problem. And finally, solution of the discretized inverse problem via explicit construction of the covariance matrix is prohibitive due to the need to solve the forward problem as many times as there are parameters. Our computational framework builds on the infinite-dimensional formulation proposed by Stuart [Acta Numer., 19 (2010), pp. 451--559] and incorporates a number of components aimed at ensuring a convergent discretization of the underlying infinite-dimensional inverse problem. The framework additionally incorporates algorithms for manipulating the prior, constructing a low rank approximation of the data-informed component of the posterior covariance operator, and exploring the posterior that together ensure scalability of the entire framework to very high parameter dimensions.  We demonstrate this computational framework on the Bayesian solution of an inverse problem in three-dimensional global seismic wave propagation with hundreds of thousands of parameters.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\PushForward Inference\Butler_et_al-Combining_Push-Forward_Measures_and_Bayes'_Rule_to_Construct_Consistent_2018.pdf}
}

@article{butler2018a,
  title = {Convergence of {{Probability Densities Using Approximate Models}} for {{Forward}} and {{Inverse Problems}} in {{Uncertainty Quantification}}},
	author = {Butler, T. and Jakeman, J. and Wildey, T.},
  year = {2018},
  journal = {SIAM Journal on Scientific Computing},
  volume = {40},
  number = {5},
  pages = {A3523-A3548},
  publisher = {{Society for Industrial and Applied Mathematics}},
  urldate = {2023-07-28},
  abstract = {We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data on quantities of interest. The solution, given as a probability measure, is derived using a Bayesian updating approach for measurable maps that finds a posterior probability measure that when propagated through the deterministic model produces a  push-forward measure that exactly matches the observed probability measure on the data. Our approach for finding such posterior measures, which we call consistent Bayesian inference or push-forward based inference, is simple and only requires the computation of the push-forward probability measure induced by the combination of a prior probability measure and the deterministic model. We establish existence and uniqueness of observation-consistent posteriors and present both stability and error analyses. We also discuss the relationships between consistent Bayesian inference, classical/statistical Bayesian inference, and a recently developed measure-theoretic approach for inference. Finally, analytical and numerical results are presented to highlight certain properties of the consistent Bayesian approach and the differences between this approach and the two aforementioned alternatives for inference.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\PushForward Inference\Butler_et_al-Convergence_of_Probability_Densities_Using_Approximate_Models_for_Forward_and_2018.pdf}
}

@article{butler2020,
  title = {Data-Consistent Inversion for Stochastic Input-to-Output Maps*},
	author = {Butler, Troy and Wildey, T. and Yen, Tian Yu},
  year = {2020},
  journal = {Inverse Problems},
  volume = {36},
  number = {8},
  pages = {085015},
  publisher = {IOP Publishing},
  urldate = {2023-07-28},
  abstract = {Data-consistent inversion is a recently developed measure-theoretic framework for solving a stochastic inverse problem involving models of physical systems. The goal is to construct a probability measure on model inputs (i.e., parameters of interest) whose associated push-forward measure matches (i.e., is consistent with) a probability measure on the observable outputs of the model (i.e., quantities of interest). Previous implementations required the map from parameters of interest to quantities of interest to be deterministic. This work generalizes this framework for maps that are stochastic, i.e., contain uncertainties and variation not explainable by variations in uncertain parameters of interest. Generalizations of previous theorems of existence, uniqueness, and stability of the data-consistent solution are provided while new theoretical results address the stability of marginals on parameters of interest. A notable aspect of the algorithmic generalization is the ability to query the solution to generate independent identically distributed samples of the parameters of interest without requiring knowledge of the so-called stochastic parameters. This work therefore extends the applicability of the data-consistent inversion framework to a much wider class of problems. This includes those based on purely experimental and field data where only a subset of conditions are either controllable or can be documented between experiments while the underlying physics, measurement errors, and any additional covariates are either uncertain or not accounted for by the researcher. Numerical examples demonstrate application of this approach to systems with stochastic sources of uncertainties embedded within the modeling of a system and a numerical diagnostic is summarized that is useful for determining if a key assumption is verified among competing choices of stochastic maps.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\PushForward Inference\Butler_et_al-Data-consistent_inversion_for_stochastic_input-to-output_maps_2020.pdf}
}

@article{byrd1995,
  title = {A Limited Memory Algorithm for Bound Constrained Optimization},
	author = {Byrd, Richard H. and Lu, Peihuang and Nocedal, Jorge and Zhu, Ciyou},
  year = {1995},
  journal = {SIAM Journal of Scientific Computing},
  volume = {16},
  pages = {1190--1208},
  abstract = {An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based on the gradient projection method and uses a limited memory BFGS matrix to approximate the Hessian of the objective function. It is shown how to take advantage of the form of the limited memory approximation to implement the algorithm efficiently. The results of numerical tests on a set of large problems are reported.},
  langid = {english}
}

@article{cadini2014,
  title = {An Improved Adaptive Kriging-Based Importance Technique for Sampling Multiple Failure Regions of Low Probability},
	author = {Cadini, F. and Santos, F. and Zio, E.},
  year = {2014},
  journal = {Reliability Engineering \& System Safety},
  volume = {131},
  pages = {109--117},
  urldate = {2023-10-28},
  abstract = {The estimation of system failure probabilities may be a difficult task when the values involved are very small, so that sampling-based Monte Carlo methods may become computationally impractical, especially if the computer codes used to model the system response require large computational efforts, both in terms of time and memory. This paper proposes a modification of an algorithm proposed in literature for the efficient estimation of small failure probabilities, which combines FORM to an adaptive kriging-based importance sampling strategy (AK-IS). The modification allows overcoming an important limitation of the original AK-IS in that it provides the algorithm with the flexibility to deal with multiple failure regions characterized by complex, non-linear limit states. The modified algorithm is shown to offer satisfactory results with reference to four case studies of literature, outperforming in general several other alternative methods of literature.},
  keywords = {Adaptive kriging,Importance sampling,Multiple failure regions,Small failure probabilities},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Reliability Analysis\\Cadini_et_al-An_improved_adaptive_kriging-based_importance_technique_for_sampling_multiple_2014.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\PXEMHHEB\\S0951832014001537.html}
}

@book{calvetti2007,
  title = {Introduction to {{Bayesian}} Scientific Computing: Ten Lectures on Subjective Computing},
  shorttitle = {Introduction to {{Bayesian}} Scientific Computing},
	author = {Calvetti, Daniela and Somersalo, Erkki},
  year = {2007},
  series = {Surveys and Tutorials in the Applied Mathematical Sciences},
  number = {2},
  publisher = {Springer},
  address = {New York},
  langid = {english},
  lccn = {QA276 .C258 2007},
  keywords = {Bayesian,Inverse problems (Differential equations),Statistics},
  annotation = {OCLC: ocn192078847},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Calvetti_Somersalo-Introduction_to_Bayesian_scientific_computing_2007.pdf}
}

@misc{capone2023,
  title = {Sharp {{Calibrated Gaussian Processes}}},
	author = {Capone, Alexandre and Pleiss, Geoff and Hirche, Sandra},
  year = {2023},
  number = {arXiv:2302.11961},
  eprint = {2302.11961},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-06-15},
  abstract = {While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees, and can be miscalibrated in practice. State-of-the-art approaches for designing calibrated models rely on inflating the Gaussian process posterior variance, which yields confidence intervals that are potentially too coarse. To remedy this, we present a calibration approach that generates predictive quantiles using a computation inspired by the vanilla Gaussian process posterior variance, but using a different set of hyperparameters, chosen to satisfy an empirical calibration constraint. This results in a calibration approach that is considerably more flexible than existing approaches. Our approach is shown to yield a calibrated model under reasonable assumptions. Furthermore, it outperforms existing approaches not only when employed for calibrated regression, but also to inform the design of Bayesian optimization algorithms.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Capone_et_al-Sharp_Calibrated_Gaussian_Processes_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\WL27U623\\2302.html}
}

@misc{casale2018,
  title = {Gaussian {{Process Prior Variational Autoencoders}}},
	author = {Casale, Francesco Paolo and Dalca, Adrian V. and Saglietti, Luca and Listgarten, Jennifer and Fusi, Nicolo},
  year = {2018},
  number = {arXiv:1810.11738},
  eprint = {1810.11738},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-10-19},
  abstract = {Variational autoencoders (VAE) are a powerful and widely-used class of models to learn complex data distributions in an unsupervised fashion. One important limitation of VAEs is the prior assumption that latent sample representations are independent and identically distributed. However, for many important datasets, such as time-series of images, this assumption is too strong: accounting for covariances between samples, such as those in time, can yield to a more appropriate model specification and improve performance in downstream tasks. In this work, we introduce a new model, the Gaussian Process (GP) Prior Variational Autoencoder (GPPVAE), to specifically address this issue. The GPPVAE aims to combine the power of VAEs with the ability to model correlations afforded by GP priors. To achieve efficient inference in this new class of models, we leverage structure in the covariance matrix, and introduce a new stochastic backpropagation strategy that allows for computing stochastic gradients in a distributed and low-memory fashion. We show that our method outperforms conditional VAEs (CVAEs) and an adaptation of standard VAEs in two image data applications.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Casale_et_al-Gaussian_Process_Prior_Variational_Autoencoders_2018.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\DNW2NZ34\\1810.html}
}

@inproceedings{cawley2011,
  title = {Baseline Methods for Active Learning},
  booktitle = {Active Learning and Experimental Design Workshop in Conjunction with {{AISTATS}} 2010},
	author = {Cawley, Gavin C.},
  year = {2011},
  volume = {16},
  pages = {47--57},
  publisher = {PMLR},
  address = {Sardinia, Italy},
  abstract = {In many potential applications of machine learning, unlabelled data are abundantly available at low cost, but there is a paucity of labelled data, and labeling unlabelled examples is expensive and/or time-consuming. This motivates the development of active learning methods, that seek to direct the collection of labelled examples such that the greatest performance gains can be achieved using the smallest quantity of labelled data. In this paper, we describe some simple pool-based active learning strategies, based on optimally regularised linear [kernel] ridge regression, providing a set of baseline submissions for the Active Learning Challenge. A simple random strategy, where unlabelled patterns are submitted to the oracle purely at random, is found to be surprisingly effective, being competitive with more complex approaches.}
}

@article{chen2008,
  title = {A {{Design-Driven Validation Approach Using Bayesian Prediction Models}}},
	author = {Chen, Wei and Xiong, Ying and Tsui, Kwok-Leung and Wang, Shuchun},
  year = {2008},
  journal = {Journal of Mechanical Design},
  volume = {130},
  number = {2},
  pages = {021101},
  urldate = {2021-09-10},
  abstract = {In most of the existing work, model validation is viewed as verifying the model accuracy, measured by the agreement between computational and experimental results. Due to the lack of resource, accuracy can only be assessed at very limited test points. However, from the design perspective, a good model should be considered the one that can provide the discrimination (with good resolution) between competing design candidates under uncertainty. In this work, a design-driven validation approach is presented. By combining data from both physical experiments and the computer model, a Bayesian approach is employed to develop a prediction model as the replacement of the original computer model for the purpose of design. Based on the uncertainty quantification with the Bayesian prediction and, subsequently, that of a design objective, some decision validation metrics are further developed to assess the confidence of using the Bayesian prediction model in making a specific design choice. We demonstrate that the Bayesian approach provides a flexible framework for drawing inferences for predictions in the intended, but maybe untested, design domain. The applicability of the proposed decision validation metrics is examined for designs with either a discrete or continuous set of design alternatives. The approach is demonstrated through an illustrative example of a robust engine piston design.},
  langid = {english},
  keywords = {Adaptive Sampling,Bayesian,Kennedy O'Hagan Framework,Model Validation,Uncertainty Quantification,Validation Metric},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Frameworks\Chen_et_al-A_Design-Driven_Validation_Approach_Using_Bayesian_Prediction_Models_2008.pdf}
}

@inproceedings{chen2012,
  title = {Probabilistic Modeling of Solder Joint Thermal Fatigue with {{Bayesian}} Method},
  booktitle = {2012 {{IEEE International Conference}} on {{Industrial Engineering}} and {{Engineering Management}}},
	author = {Chen, Ying and Xie, Limei and Kang, {\relax Rui}.},
  year = {2012},
  pages = {787--791},
  abstract = {Solder joint thermal fatigue failure is a major cause for the failure of the electronic packaging. It is influenced by the device geometry, material fatigue properties, temperature stress and other parameters. All of these parameters contain uncertainties, whereas Coffin-Manson model which is widely used to evaluate fatigue life does not take uncertainties of model parameters into consideration. In this paper, a probabilistic physics of failure (PPoF) of solder joint thermal fatigue using Bayesian theory to update parameters is put forward. Comprehensively considering the influences of uncertainties of all parameters on solder joint failure, and using Monte Carlo method to solve PPoF model, probability density function for single point failure can be obtained. Through establishing the relationship between the probability of failure and time, stress, structure and materials, this method provides a new way for reliability prediction.},
  keywords = {Bayes methods,Bayesian method,Fatigue,Probabilistic logic,Probabilistic Physics-of-Failure,Reliability,Solder joint,Soldering,Thermal fatigue,Uncertainty},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Lifetime Coffin Manson\\Chen_et_al-Probabilistic_modeling_of_solder_joint_thermal_fatigue_with_Bayesian_method_2012.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\SEIL72QD\\6837847.html}
}

@inproceedings{chen2016,
  title = {{{XGBoost}}: {{A Scalable Tree Boosting System}}},
  shorttitle = {{{XGBoost}}},
  booktitle = {Proceedings of the 22nd {{ACM SIGKDD International Conference}} on {{Knowledge Discovery}} and {{Data Mining}}},
	author = {Chen, Tianqi and Guestrin, Carlos},
  year = {2016},
  eprint = {1603.02754},
  primaryclass = {cs},
  pages = {785--794},
  urldate = {2024-02-05},
  abstract = {Tree boosting is a highly effective and widely used machine learning method. In this paper, we describe a scalable end-to-end tree boosting system called XGBoost, which is used widely by data scientists to achieve state-of-the-art results on many machine learning challenges. We propose a novel sparsity-aware algorithm for sparse data and weighted quantile sketch for approximate tree learning. More importantly, we provide insights on cache access patterns, data compression and sharding to build a scalable tree boosting system. By combining these insights, XGBoost scales beyond billions of examples using far fewer resources than existing systems.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Chen_Guestrin-XGBoost_2016.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\W2MQVDIS\\1603.html}
}

@article{chen2021,
  title = {An Effective Gradient and Geometry Enhanced Sequential Sampling Approach for {{Kriging}} Modeling},
	author = {Chen, Xiaoqian and Zhang, Yi and Zhou, Weien and Yao, Wen},
  year = {2021},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {64},
  number = {6},
  pages = {3423--3438},
  urldate = {2022-01-02},
  abstract = {Surrogates have been widely used for replacing computationally costly computer simulations. To improve the prediction accuracy with less sampling cost, sequential sampling is often used to seek targeted training samples for surrogate modeling. Previous methods often integrate gradient information to improve the sampling effect, but the increase of prediction accuracy is still limited for complicated problems. It is intractable how to better exploit the useful gradient information to sample potential highly nonlinear regions. In this paper, an effective gradient and geometry enhanced Kriging sequential sampling approach is proposed to handle this problem. First, a novel improvement function, which combines the approximate gradient and prediction variance, is constructed to measure the improvement of a candidate sampling point. Second, the design domain is partitioned into multiple Voronoi subdomains according to design points, and an adaptive and efficient crossvalidation-based criterion is introduced to determine the candidate sampling regions and reduce the optimization cost. Finally, the improvement function is maximized in the selected Voronoi subdomains to sample a new point, which can effectively achieve great accuracy improvement in the nonlinear area. The proposed approach is tested on several highly nonlinear functions and an application-related example, and the experimental results confirm its effectiveness.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Chen_et_al-An_effective_gradient_and_geometry_enhanced_sequential_sampling_approach_for_2021.pdf}
}

@article{chicco2021,
  title = {The Coefficient of Determination {{R-squared}} Is More Informative than {{SMAPE}}, {{MAE}}, {{MAPE}}, {{MSE}} and {{RMSE}} in Regression Analysis Evaluation},
	author = {Chicco, Davide and Warrens, Matthijs J. and Jurman, Giuseppe},
  year = {2021},
  journal = {PeerJ Computer Science},
  volume = {7},
  urldate = {2022-08-05},
  abstract = {Regression analysis makes up a large part of supervised machine learning, and consists of the prediction of a continuous independent target from a set of other predictor variables. The difference between binary classification and regression is in the target range: in binary classification, the target can have only two values (usually encoded as 0 and 1), while in regression the target can have multiple values. Even if regression analysis has been employed in a huge number of machine learning studies, no consensus has been reached on a single, unified, standard metric to assess the results of the regression itself. Many studies employ the mean square error (MSE) and its rooted variant (RMSE), or the mean absolute error (MAE) and its percentage variant (MAPE). Although useful, these rates share a common drawback: since their values can range between zero and +infinity, a single value of them does not say much about the performance of the regression with respect to the distribution of the ground truth elements. In this study, we focus on two rates that actually generate a high score only if the majority of the elements of a ground truth group has been correctly predicted: the coefficient of determination (also known as               R               -squared or               R               2               ) and the symmetric mean absolute percentage error (SMAPE). After showing their mathematical properties, we report a comparison between               R               2               and SMAPE in several use cases and in two real medical scenarios. Our results demonstrate that the coefficient of determination (               R               -squared) is more informative and truthful than SMAPE, and does not have the interpretability limitations of MSE, RMSE, MAE and MAPE. We therefore suggest the usage of               R               -squared as standard metric to evaluate regression analyses in any scientific domain.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Chicco_et_al-The_coefficient_of_determination_R-squared_is_more_informative_than_SMAPE,_MAE,_2021.pdf}
}

@book{choi2007,
  title = {Reliability-Based Structural Design},
	author = {Choi, Seung-Kyum and Grandhi, R. V. and Canfield, Robert A.},
  year = {2007},
  publisher = {Springer},
  address = {London},
  langid = {english},
  lccn = {TA658.8 .C48 2007},
  keywords = {Mathematics,Reliability (Engineering),Structural optimization},
  annotation = {OCLC: ocm70402813},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Choi_et_al-Reliability-based_structural_design_2007.pdf}
}

@inproceedings{chua2018,
  title = {Deep {{Reinforcement Learning}} in a {{Handful}} of {{Trials}} Using {{Probabilistic Dynamics Models}}},
  booktitle = {32nd {{Conference}} on {{Neural Information Processing Systems}}},
	author = {Chua, Kurtland and Calandra, Roberto and McAllister, Rowan and Levine, Sergey},
  year = {2018},
  pages = {4759--4770},
  address = {Montr{\'e}al, Canada},
  urldate = {2022-05-24},
  abstract = {Model-based reinforcement learning (RL) algorithms can attain excellent sample efficiency, but often lag behind the best model-free algorithms in terms of asymptotic performance. This is especially true with high-capacity parametric function approximators, such as deep networks. In this paper, we study how to bridge this gap, by employing uncertainty-aware dynamics models. We propose a new algorithm called probabilistic ensembles with trajectory sampling (PETS) that combines uncertainty-aware deep network dynamics models with sampling-based uncertainty propagation. Our comparison to state-of-the-art model-based and model-free deep RL algorithms shows that our approach matches the asymptotic performance of model-free algorithms on several challenging benchmark tasks, while requiring significantly fewer samples (e.g., 8 and 125 times fewer samples than Soft Actor Critic and Proximal Policy Optimization respectively on the half-cheetah task).},
  langid = {english},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning,Computer Science - Robotics,Statistics - Machine Learning},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\WBN47YID\1805.html}
}

@article{chun2024,
  title = {Active Learning-Based Kriging Model with Noise Responses and Its Application to Reliability Analysis of Structures},
	author = {Chun, Junho},
  year = {2024},
  journal = {Applied Sciences},
  volume = {14},
  number = {2},
  abstract = {This study introduces a reliability analysis methodology employing Kriging modeling enriched by a hybrid active learning process. Emphasizing noise integration into structural response predictions, this research presents a framework that combines Kriging modeling with regression to handle noisy data. The framework accommodates either constant variance of noise for all observed responses or varying, uncorrelated noise variances. Hyperparameters and the variance of the Kriging model with noisy data are determined through maximum likelihood estimation to address inherent uncertainties in structural predictions. An adaptive hybrid learning function guides design of experiment (DoE) point identification through an iterative enrichment process. This function strategically targets points near the limit-state approximation, farthest from existing training points, and explores candidate points to maximize the probability of misclassification. The framework's application is demonstrated through metamodel-based reliability analysis for continuum and discrete structures with relatively large degrees of freedom, employing subset simulations. Numerical examples validate the framework's effectiveness, highlighting its potential for accurate and efficient reliability assessments in complex structural systems.}
}

@inbook{cohen2011,
  title = {Integration},
  booktitle = {Numerical {{Approximation Methods}}},
	author = {Cohen, Harold},
  year = {2011},
  pages = {105--168},
  publisher = {Springer New York},
  address = {New York, NY},
  urldate = {2022-03-15},
  collaborator = {Cohen, Harold},
  langid = {english}
}

@article{contreras2014,
  title = {An Improved Variant of the Conventional {{Harmony Search}} Algorithm},
	author = {Contreras, Jhonatan and Amaya, Iv{\'a}n and Correa, Rodrigo},
  year = {2014},
  journal = {Applied Mathematics and Computation},
  volume = {227},
  pages = {821--830},
  urldate = {2022-03-28},
  langid = {english}
}

@article{cortes1995,
  title = {Support-Vector Networks},
	author = {Cortes, Corinna and Vapnik, Vladimir},
  year = {1995},
  journal = {Machine Learning},
  volume = {20},
  number = {3},
  pages = {273--297},
  urldate = {2022-01-21},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Cortes_Vapnik-Support-vector_networks_1995.pdf}
}

@article{cowen-rivers2022,
  title = {{{HEBO}}: {{Pushing The Limits}} of {{Sample-Efficient Hyper-parameter Optimisation}}},
  shorttitle = {{{HEBO}}},
	author = {{Cowen-Rivers}, Alexander I. and Lyu, Wenlong and Tutunov, Rasul and Wang, Zhi and Grosnit, Antoine and others},
  year = {2022},
  journal = {Journal of Artificial Intelligence Research},
  volume = {74},
  pages = {1269--1349},
  urldate = {2024-02-08},
  abstract = {In this work we rigorously analyse assumptions inherent to black-box optimisation hyper-parameter tuning tasks. Our results on the Bayesmark benchmark indicate that heteroscedasticity and non-stationarity pose significant challenges for black-box optimisers. Based on these findings, we propose a Heteroscedastic and Evolutionary Bayesian Optimisation solver (HEBO). HEBO performs non-linear input and output warping, admits exact marginal log-likelihood optimisation and is robust to the values of learned parameters. We demonstrate HEBO's empirical efficacy on the NeurIPS 2020 Black-Box Optimisation challenge, where HEBO placed first. Upon further analysis, we observe that HEBO significantly outperforms existing black-box optimisers on 108 machine learning hyperparameter tuning tasks comprising the Bayesmark benchmark. Our findings indicate that the majority of hyper-parameter tuning tasks exhibit heteroscedasticity and non-stationarity, multiobjective acquisition ensembles with Pareto front solutions improve queried configurations, and robust acquisition maximisers afford empirical advantages relative to their non-robust counterparts. We hope these findings may serve as guiding principles for practitioners of Bayesian optimisation.},
  copyright = {Copyright (c)},
  langid = {english},
  keywords = {automated reasoning,bayesian optimization,hyperparameter tuning,uncertainty},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Optimization\BO\Cowen-Rivers_et_al-HEBO_2022.pdf}
}

@article{cremanns2017,
  title = {Deep {{Gaussian Covariance Network}}},
	author = {Cremanns, Kevin and Roos, Dirk},
  year = {2017},
  journal = {arXiv:1710.06202},
  eprint = {1710.06202},
  urldate = {2021-09-07},
  abstract = {The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and thus invariant to the translations in the input space. The optimization of the hyperparameters is commonly done by maximizing the log marginal likelihood. This works quite well, if the distances are uniform distributed. In the case of a locally adapted or even sparse input space, the prediction of a test point can be worse dependent of its position. A possible solution to this, is the usage of a non-stationary covariance function, where the hyperparameters are calculated by a deep neural network. So that the correlation length scales and possibly the noise variance are dependent on the test point. Furthermore, different types of covariance functions are trained simultaneously, so that the Gaussian process prediction is an additive overlay of different covariance matrices. The right covariance functions combination and its hyperparameters are learned by the deep neural network. Additional, the Gaussian process will be able to be trained by batches or online and so it can handle arbitrarily large data sets. We call this framework Deep Gaussian Covariance Network (DGCP). There are also further extensions to this framework possible, for example sequentially dependent problems like time series or the local mixture of experts. The basic framework and some extension possibilities will be presented in this work. Moreover, a comparison to some recent state of the art surrogate model methods will be performed, also for a time dependent problem.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Gaussian processes,Machine learning,Neuronal Network},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\IMH\Cremanns_Roos-Deep_Gaussian_Covariance_Network_2017.pdf}
}

@phdthesis{cremanns2021,
  title = {Probabilistic Machine Learning for Pattern Recognition and Design Exploration},
	author = {Cremanns, Kevin},
  year = {2021},
  urldate = {2021-09-07},
  abstract = {The following thesis deals with the development of new probabilistic machine learning models with a focus on efficiency, flexibility, applicability, scalability and high prediction accuracy. Therefore, learning tasks from the areas of regression, classification, image classification, time series as well as the representation of spatial and / or temporally correlated quantities are examined. In order to achieve these goals and in addition to the development of the models themselves, their interaction to the field of data generation is also investigated. The calculable uncertainty of the probabilistic models is used to obtain the maximum information gain with as few data points as possible. This methodology is also used for the efficient solving of optimization problems. Besides obtaining an accurate approximation model of the data, a deeper understanding of the correlations between input and output is desired, therefore the topic of sensitivity analysis is a further part of this work. The developed probabilistic models are used to evaluate the number of calculations needed to estimate the sensitivities as efficiently as possible, even for correlated inputs.},
  collaborator = {Reh, Stefan and M{\"u}nstermann, Sebastian and Roos, Dirk},
  langid = {english},
  school = {RWTH Aachen University},
  keywords = {Adaptive Sampling,Bayesian Optimization,Classification,Deep Networks,Design of Experiments,Gaussian processes,Kriging,Latin Hypercube Sampling,Machine learning,Regression,Sensitivity Analysis},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\IMH\Cremanns-Probabilistic_machine_learning_for_pattern_recognition_and_design_exploration_2021.pdf}
}

@article{crombecq2011,
  title = {A {{Novel Hybrid Sequential Design Strategy}} for {{Global Surrogate Modeling}} of {{Computer Experiments}}},
	author = {Crombecq, Karel and Gorissen, Dirk and Deschrijver, Dirk and Dhaene, Tom},
  year = {2011},
  journal = {SIAM Journal on Scientific Computing},
  volume = {33},
  number = {4},
  pages = {1948--1974},
  urldate = {2022-02-14},
  langid = {english}
}

@book{cursi2015,
  title = {Uncertainty Quantification and Stochastic Modeling with {{Matlab}}},
	author = {de Cursi, Eduardo Souza and Sampaio, Rubens},
  year = {2015},
  series = {Numerical Methods in Engineering},
  publisher = {ISTE Press},
  address = {London},
  langid = {english},
  keywords = {Statistics,Uncertainty Quantification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Cursi_Sampaio-Uncertainty_quantification_and_stochastic_modeling_with_Matlab_2015.pdf}
}

@book{dahmen2008,
  title = {{Numerik f{\"u}r Ingenieure und Naturwissenschaftler}},
	author = {Dahmen, Wolfgang and Reusken, Arnold},
  year = {2008},
  series = {{Springer-Lehrbuch}},
  edition = {2., korrigierte Aufl},
  publisher = {Springer},
  address = {Berlin Heidelberg},
  abstract = {Verlagstext: Dieses Lehrbuch bietet eine Einf{\"u}hrung in alle wesentlichen grundlegenden numerischen Methodenbausteine, wobei in einem abschliessenden Kapitel die Kombination dieser Bausteine anhand komplexerer Anwendungsbeispiele illustriert wird. Den einzelnen Themen wird eine durch zahlreiche Beispiele untermauerte Diskussion der Begriffe Kondition und Stabilit{\"a}t vorausgeschickt, die dann als verbindende Orientierungslinie dienen. Ebenso wie die gestaffelte Aufbereitung der Themen, wobei einfachen Grundelementen {\"u}berspringbare vertiefende Abhandlungen folgen, soll dies helfen, einen Grad von Anwendungs- und Beurteilungsverst{\"a}ndnis zu entwickeln, das ein steigender und flexibler Einsatzbedarf numerischer Methoden in Ingenieur- und Naturwissenschaften erfordert. Je nach Ausbaustufe kann daher das Buch sowohl als Grundlage einer einsemestrigen einf{\"u}hrenden als auch einer weiterf{\"u}hrenden Numerik-Vorlesung im Ingenieurstudium dienen und eignet sich dar{\"u}ber hinaus f{\"u}r die Numerikausbildung im Mathematikstudium},
  langid = {german},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\EMPTY_COLLECTION_NAME\Dahmen_Reusken-Numerik_fur_Ingenieure_und_Naturwissenschaftler_2008.pdf}
}

@book{dahmen2008a,
  title = {{Numerik f{\"u}r Ingenieure und Naturwissenschaftler}},
	author = {Dahmen, Wolfgang and Reusken, Arnold},
  year = {2008},
  series = {{Springer-Lehrbuch}},
  edition = {2., korrigierte Aufl},
  publisher = {Springer},
  address = {Berlin Heidelberg},
  abstract = {Verlagstext: Dieses Lehrbuch bietet eine Einf{\"u}hrung in alle wesentlichen grundlegenden numerischen Methodenbausteine, wobei in einem abschliessenden Kapitel die Kombination dieser Bausteine anhand komplexerer Anwendungsbeispiele illustriert wird. Den einzelnen Themen wird eine durch zahlreiche Beispiele untermauerte Diskussion der Begriffe Kondition und Stabilit{\"a}t vorausgeschickt, die dann als verbindende Orientierungslinie dienen. Ebenso wie die gestaffelte Aufbereitung der Themen, wobei einfachen Grundelementen {\"u}berspringbare vertiefende Abhandlungen folgen, soll dies helfen, einen Grad von Anwendungs- und Beurteilungsverst{\"a}ndnis zu entwickeln, das ein steigender und flexibler Einsatzbedarf numerischer Methoden in Ingenieur- und Naturwissenschaften erfordert. Je nach Ausbaustufe kann daher das Buch sowohl als Grundlage einer einsemestrigen einf{\"u}hrenden als auch einer weiterf{\"u}hrenden Numerik-Vorlesung im Ingenieurstudium dienen und eignet sich dar{\"u}ber hinaus f{\"u}r die Numerikausbildung im Mathematikstudium},
  langid = {german},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Numerics\Dahmen_Reusken-Numerik_fur_Ingenieure_und_Naturwissenschaftler_2008.pdf}
}

@article{dalmasso2020,
  title = {Conditional {{Density Estimation Tools}} in {{Python}} and {{R}} with {{Applications}} to {{Photometric Redshifts}} and {{Likelihood-Free Cosmological Inference}}},
	author = {Dalmasso, Niccol{\`o} and Pospisil, Taylor and Lee, Ann B. and Izbicki, Rafael and Freeman, Peter E. and others},
  year = {2020},
  journal = {Astronomy and Computing},
  volume = {30},
  eprint = {1908.11523},
  primaryclass = {astro-ph, stat},
  pages = {100362},
  urldate = {2023-02-04},
  abstract = {It is well known in astronomy that propagating non-Gaussian prediction uncertainty in photometric redshift estimates is key to reducing bias in downstream cosmological analyses. Similarly, likelihood-free inference approaches, which are beginning to emerge as a tool for cosmological analysis, require a characterization of the full uncertainty landscape of the parameters of interest given observed data. However, most machine learning (ML) or training-based methods with open-source software target point prediction or classification, and hence fall short in quantifying uncertainty in complex regression and parameter inference settings. As an alternative to methods that focus on predicting the response (or parameters) \${\textbackslash}mathbf\{y\}\$ from features \${\textbackslash}mathbf\{x\}\$, we provide nonparametric conditional density estimation (CDE) tools for approximating and validating the entire probability density function (PDF) \${\textbackslash}mathrm\{p\}({\textbackslash}mathbf\{y\}{\textbar}{\textbackslash}mathbf\{x\})\$ of \${\textbackslash}mathbf\{y\}\$ given (i.e., conditional on) \${\textbackslash}mathbf\{x\}\$. As there is no one-size-fits-all CDE method, the goal of this work is to provide a comprehensive range of statistical tools and open-source software for nonparametric CDE and method assessment which can accommodate different types of settings and be easily fit to the problem at hand. Specifically, we introduce four CDE software packages in \${\textbackslash}texttt\{Python\}\$ and \${\textbackslash}texttt\{R\}\$ based on ML prediction methods adapted and optimized for CDE: \${\textbackslash}texttt\{NNKCDE\}\$, \${\textbackslash}texttt\{RFCDE\}\$, \${\textbackslash}texttt\{FlexCode\}\$, and \${\textbackslash}texttt\{DeepCDE\}\$. Furthermore, we present the \${\textbackslash}texttt\{cdetools\}\$ package, which includes functions for computing a CDE loss function for tuning and assessing the quality of individual PDFs, along with diagnostic functions. We provide sample code in \${\textbackslash}texttt\{Python\}\$ and \${\textbackslash}texttt\{R\}\$ as well as examples of applications to photometric redshift estimation and likelihood-free cosmological inference via CDE.},
  archiveprefix = {arxiv},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,Statistics - Computation,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Statistics\\Dalmasso_et_al-Conditional_Density_Estimation_Tools_in_Python_and_R_with_Applications_to_2020.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\RW4PGFZT\\1908.html}
}

@inproceedings{damianou2013,
  title = {Deep {{Gaussian}} Processes},
  booktitle = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics},
	author = {Damianou, Andreas and Lawrence, Neil D.},
  year = {2013},
  series = {Proceedings of Machine Learning Research},
  volume = {31},
  pages = {207--215},
  publisher = {PMLR},
  address = {Scottsdale, Arizona, USA},
  abstract = {In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples.}
}

@article{danquah2022,
  title = {Potential of Statistical Model Verification, Validation and Uncertainty Quantification in Automotive Vehicle Dynamics Simulations: A Review},
  shorttitle = {Potential of Statistical Model Verification, Validation and Uncertainty Quantification in Automotive Vehicle Dynamics Simulations},
	author = {Danquah, Benedikt and Riedmaier, Stefan and Lienkamp, Markus},
  year = {2022},
  journal = {Vehicle System Dynamics},
  volume = {60},
  number = {4},
  pages = {1292--1321},
  publisher = {Taylor \& Francis},
  urldate = {2023-02-04},
  abstract = {The modelling, simulation and analysis methods in automotive development are in the process of transformation. Increasing system complexity, variant diversity and efforts to improve efficiency lead to more complex simulations and depend on virtual vehicle development, testing and approval across a large application area. Consequently, the new key requirements of modern validation involve more precise reliability quantification of large application areas, achieved with reasonable effort of cost and time. This paper identifies that the neglection of uncertainties, low information in validation results, low extrapolation capability and the resulting small application area are preventing the state-of-the-art validation meeting those new requirements. In an extensive analysis examining more than twenty frameworks in detail, this paper shows that statistical methods exhibit a high potential to remedy these four key insufficiencies. The paper justifies comprehensively that consistent statistical validation is necessary, important and crucial for precise reliability quantification, which enables accurate model selection, knowledge building and decision making in modern automotive vehicle-dynamics simulations. An example is given explaining the basic principle and benefit of consistent statistical validation. Since automotive statistical methods are still at the beginning, the aim is to enable further investigation by showing their potential and providing deeper knowledge about this topic.},
  keywords = {automotive vehicle,Modelling and simulation,statistics,uncertainty quantification,validation,verification}
}

@inproceedings{darveaux2000,
  title = {Effect of Simulation Methodology on Solder Joint Crack Growth Correlation},
  booktitle = {2000 {{Proceedings}}. 50th {{Electronic Components}} and {{Technology Conference}} ({{Cat}}. {{No}}.{{00CH37070}})},
	author = {Darveaux, R.},
  year = {2000},
  pages = {1048--1058},
  abstract = {A generalized solder joint fatigue life model for surface mount packages was previously published by the author. The model is based on correlation to measured crack growth data on BGA joints during thermal cycling. It was subsequently discovered by Anderson et. al. that the ANSYS/sup TM/ 5.2 finite element code used in the model had an error in its method for calculating plastic work. It was shown that significant error in life prediction could result by using a recent version of the code where the bug has been fixed. The error comes about since the original crack growth constants were derived based on plastic work calculations that had the bug. In this paper, crack initiation and growth constants are recalculated using ANSYS/sup TM/ 5.6. In addition, several other model related issues are explored with respect to the crack growth correlations. For example, 3D slice models were compared to quarter symmetry models. Anand's constitutive model was compared with Darveaux's constitutive model. It was shown that the crack growth rate dependence on strain energy density always had an exponent of 1.10+/-0.15. This is in the range of the original correlation, so the accuracy of relative predictions should still be within+/-25\%. However, the accuracy of absolute predictions could be off by a factor of 7 in the worst case, if the analyst uses a modeling procedure that is not consistent with that used for the crack growth correlation. The key to good accuracy is to maintain consistency in the modeling procedure.},
  keywords = {Accuracy,Capacitive sensors,Creep,Fatigue,Finite element methods,Packaging,Plastics,Soldering,Steady-state,Surface cracks},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Lifetime Coffin Manson\\Darveaux-Effect_of_simulation_methodology_on_solder_joint_crack_growth_correlation_2000.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\HXTHCIUX\\853299.html}
}

@book{deierlein2019,
  title = {State-of-{{Art}} in {{Computational Simulation}} for {{Natural Hazards Engineering}}},
	author = {Deierlein, Gregory and Zsarn{\'o}czay, {\'A}d{\'a}m and Arduino, Pedro and Baker, Jack and Bray, Jonathan and others},
  year = {2019},
  abstract = {This report is a product of the NSF NHERI SimCenter and provides an overview and review of simulation requirements and software tools for natural hazards engineering of the built environment. The simulations discussed in this report are an essential component of research to address the three grand challenge areas and associated research questions outlined in the NHERI Science Plan (2017). As outlined in the NHERI Science Plan, the grand challenges entail: (1) quantifying natural hazards and their effects on civil infrastructure; (2) evaluating the vulnerability of civil infrastructure and social vulnerability of populations in at-risk communities; and (3) creation of technologies and tools to design and implement measures to promote resilience to natural hazards. Accordingly, required simulation technologies encompass a broad range of phenomena and considerations, from characterization and simulation of natural hazards and their damaging effects on buildings and civil infrastructure, to quantifying the resulting economic losses, disruption, and other consequences on society. Ultimately, the goal is to enable high-fidelity and high-resolution models in regional simulations that can support technological, economic, and policy solutions to mitigate the threat of natural hazards. The natural hazards addressed in this report include earthquakes, tsunami, storm and tornado winds, and storm surge. While not an exhaustive list of all possible natural hazards, these are the hazards addressed under the U.S. National Science Foundation's (NSF) NHERI research program. The report is organized in a sequential fashion, including: (1) simulation methods to characterize the natural hazards; (2) response simulation of structural and geotechnical systems and localized wind and water flows; and (3) quantifying the resulting damage and its effects on the performance of buildings, transportation systems, and utility infrastructure systems. Given the inherent uncertainties in all aspects of natural hazards engineering, methods of uncertainty propagation are reviewed, with an eye toward their broad applicability within and between the various simulation components. Owing to the broad scope of the simulation topics, this state-of-art review is presented with the goal of educating and informing researchers, including both simulation tool developers and users, on key requirements and capabilities within each simulation topic. The report is also a guide for the development of simulation capabilities by the NSF NHERI SimCenter. Each section of the report begins with a brief overview of the purpose of the simulation component, including a discussion of the goals of the analysis (what is being calculated), the underlying physics or principles involved in the simulation, common modeling assumptions and simplifications, and typical input and output of the simulations. With the aim to take stock of computational simulation capabilities, inform research by the NHERI research community, and position the work of the NHERI SimCenter, the summaries identify and review commonly used simulation software that is widely known and used for research in academia and industry. Particular emphasis is placed on open-source or other software that is hosted on DesignSafe or is otherwise easily accessible to researchers, and a summary table of the simulation software tools is provided as an appendix to the report. In addition to summarizing the state-of-art in the various topic areas, each section of the report identifies major research gaps and needs, with the intent that these could motivate research proposals to NSF or other agencies that will lead to future advancements. The final chapter of the report summarizes how tools being developed by NHERI SimCenter are advancing the state-of-art in simulating the effects of natural hazards on the built environment. This report is intended to be a living document series, which will be updated regularly based on feedback from the research community and advancements in simulation technologies for natural hazards engineering.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Optimization\Deierlein_et_al-State-of-Art_in_Computational_Simulation_for_Natural_Hazards_Engineering_2019.pdf}
}

@misc{depeweg2018,
  title = {Decomposition of {{Uncertainty}} in {{Bayesian Deep Learning}} for {{Efficient}} and {{Risk-sensitive Learning}}},
	author = {Depeweg, Stefan and {Hern{\'a}ndez-Lobato}, Jos{\'e} Miguel and {Doshi-Velez}, Finale and Udluft, Steffen},
  year = {2018},
  number = {arXiv:1710.07283},
  eprint = {1710.07283},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-01-27},
  abstract = {Bayesian neural networks with latent variables are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns in the data. We show how to extract and decompose uncertainty into epistemic and aleatoric components for decision-making purposes. This allows us to successfully identify informative points for active learning of functions with heteroscedastic and bimodal noise. Using the decomposition we further define a novel risk-sensitive criterion for reinforcement learning to identify policies that balance expected cost, model-bias and noise aversion.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\EMPTY_COLLECTION_NAME\\Depeweg_et_al-Decomposition_of_Uncertainty_in_Bayesian_Deep_Learning_for_Efficient_and_2018.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\5Z7GG9CK\\1710.html}
}

@misc{depeweg2018a,
  title = {Decomposition of {{Uncertainty}} in {{Bayesian Deep Learning}} for {{Efficient}} and {{Risk-sensitive Learning}}},
	author = {Depeweg, Stefan and {Hern{\'a}ndez-Lobato}, Jos{\'e} Miguel and {Doshi-Velez}, Finale and Udluft, Steffen},
  year = {2018},
  number = {arXiv:1710.07283},
  eprint = {1710.07283},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-01-27},
  abstract = {Bayesian neural networks with latent variables are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns in the data. We show how to extract and decompose uncertainty into epistemic and aleatoric components for decision-making purposes. This allows us to successfully identify informative points for active learning of functions with heteroscedastic and bimodal noise. Using the decomposition we further define a novel risk-sensitive criterion for reinforcement learning to identify policies that balance expected cost, model-bias and noise aversion.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Uncertainty Quantification\\Depeweg_et_al-Decomposition_of_Uncertainty_in_Bayesian_Deep_Learning_for_Efficient_and_2018.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\V97BBBG9\\1710.html}
}

@article{depiver2021,
  title = {Thermal Fatigue Life of Ball Grid Array ({{BGA}}) Solder Joints Made from Different Alloy Compositions},
	author = {Depiver, Joshua A. and Mallik, Sabuj and Amalu, Emeka H.},
  year = {2021},
  journal = {Engineering Failure Analysis},
  volume = {125},
  pages = {105447},
  urldate = {2023-05-30},
  abstract = {As temperature cycling drives fatigue failure of solder joints in electronic modules, characterisation of the thermal fatigue response of different solder alloy formulations in BGA solder joints functioning in mission-critical systems has become crucial. Four different lead-free and one eutectic lead-based solder alloys in BGA solder joints are characterised against their thermal fatigue lives (TFLs) to predict their mean-time-to-failure for preventive maintenance advice. Five finite elements (FE) models of the assemblies of the BGAs with the different solder alloy compositions are created with SolidWorks. The models are subjected to standard IEC 60749--25 temperature cycling in ANSYS mechanical package environment. Plastic strain, shear strain, plastic shear strain, and accumulated creep energy density responses of the solder joints are obtained and inputted into established life prediction models -- Coffin Manson, Engelmaier, Solomon and Syed -- to determine the lives of the models. SAC405 joints have the highest predicted TFL of circa 13.2~years, while SAC387 joints have the least life of circa 1.4~years. The predicted lives are inversely proportional to the magnitude of the areas of stress--strain hysteresis loops of the BGA solder joints. The prediction models are significantly not consistent in predicted magnitudes of TFLs across the solder joints. With circa 838\% variation in the magnitudes of TFL predicted for Sn63Pb37, the damage parameters used in the models played a critical role and justifies that a combination of several failure modes drives solder joints damage. This research provides a technique for determining the preventive maintenance time of BGA components in mission-critical systems. It proposes developing a new life prediction model based on a combination of the damage parameters for improved prediction.},
  langid = {english},
  keywords = {Anand model,Creep,Fatigue ductility,Hysteresis loop,Life prediction models,Plastic shear strain,Shear strain,Solder damage parameters,Thermal fatigue life},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Lifetime Coffin Manson\\Depiver_et_al-Thermal_fatigue_life_of_ball_grid_array_(BGA)_solder_joints_made_from_different_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\6P5W8X4W\\S1350630721003071.html}
}

@article{dourado2021,
  title = {A {{Nonstationary Uncertainty Model}} and {{Bayesian Calibration}} of {{Strain-Life Models}}},
	author = {Dourado, Arinan and Irmak, Firat and Viana, Felipe A. C. and Gordon, Ali P.},
  year = {2021},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {6},
  number = {1},
  pages = {011002},
  urldate = {2023-05-04},
  abstract = {Abstract             The Coffin--Manson--Basquin--Haford (CMBH) model is a well-accepted strain-life relationship to model fatigue life as a function of applied strain. In this paper, we propose a nonstationary uncertainty model for the CMBH model, alongside a Bayesian framework for model calibration and estimation of confidence and prediction intervals. Using Inconel 617 coupon test data, we compared our approach to traditional stationary variance models. The proposed uncertainty model successfully captures the fact that the variance of strain amplitude decreases with increasing fatigue life. Additionally, a discussion on how to use the proposed Bayesian framework to compensate for the lack of data by using prior information coming from similar alloys is also presented considering Hastealloy-X and Inconel 617 coupon data.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\JUHE5C9Z\Dourado et al. - 2021 - A Nonstationary Uncertainty Model and Bayesian Cal.pdf}
}

@article{dourado2021a,
  title = {A {{Nonstationary Uncertainty Model}} and {{Bayesian Calibration}} of {{Strain-Life Models}}},
	author = {Dourado, Arinan and Irmak, Firat and Viana, Felipe A. C. and Gordon, Ali P.},
  year = {2021},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {6},
  number = {011002},
  urldate = {2023-05-30},
  abstract = {The Coffin--Manson--Basquin--Haford (CMBH) model is a well-accepted strain-life relationship to model fatigue life as a function of applied strain. In this paper, we propose a nonstationary uncertainty model for the CMBH model, alongside a Bayesian framework for model calibration and estimation of confidence and prediction intervals. Using Inconel 617 coupon test data, we compared our approach to traditional stationary variance models. The proposed uncertainty model successfully captures the fact that the variance of strain amplitude decreases with increasing fatigue life. Additionally, a discussion on how to use the proposed Bayesian framework to compensate for the lack of data by using prior information coming from similar alloys is also presented considering Hastealloy-X and Inconel 617 coupon data.},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\JJWZ9QID\A-Nonstationary-Uncertainty-Model-and-Bayesian.html}
}

@article{dowding2008,
  title = {Formulation of the Thermal Problem},
	author = {Dowding, Kevin J. and Pilch, Martin and Hills, Richard G.},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2385--2389},
  urldate = {2021-09-07},
  abstract = {This paper describes the thermal problem and presents the experimental data for validation. The thermal problem involves validating a model for heat conduction in a solid. The mathematical model is based on one-dimensional, linear heat conduction in a solid slab, with heat flux boundary conditions. Experimental data from a series of material characterization, validation, and accreditation experiments related to the mathematical model are provided. The objective is to use the series of experiments to assess the model, and then use the model to predict regulatory performance relative to a regulatory requirement. The regulatory requirement is defined in terms of the probability that a surface temperature not exceed a specified temperature at the regulatory conditions.},
  langid = {english},
  keywords = {Examples,Model Validation,Sandia Workshop,Validation Problem},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\ValidationWS Sandia Lab\Dowding_et_al-Formulation_of_the_thermal_problem_2008.pdf}
}

@article{dowding2008a,
  title = {Validation Challenge Workshop Summary},
	author = {Dowding, Kevin J. and {Red-Horse}, John R. and Paez, Thomas L. and Babu{\v s}ka, Ivo M. and Hills, Richard G. and others},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2381--2384},
  urldate = {2021-09-07},
  abstract = {Comput. Methods Appl. Mech. Engrg. 197 (29--32) (2008) 2490--2495.},
  langid = {english},
  keywords = {Model Validation,Sandia Workshop},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\ValidationWS Sandia Lab\Dowding_et_al-Validation_challenge_workshop_summary_2008.pdf}
}

@article{dubourg2013,
  title = {Metamodel-Based Importance Sampling for Structural Reliability Analysis},
	author = {Dubourg, V. and Sudret, B. and Deheeger, F.},
  year = {2013},
  journal = {Probabilistic Engineering Mechanics},
  volume = {33},
  pages = {47--57},
  urldate = {2024-01-28},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Reliability Analysis\Dubourg_et_al-Metamodel-based_importance_sampling_for_structural_reliability_analysis_2013.pdf}
}

@misc{dutordoir2023,
  title = {Neural {{Diffusion Processes}}},
	author = {Dutordoir, Vincent and Saul, Alan and Ghahramani, Zoubin and Simpson, Fergus},
  year = {2023},
  number = {arXiv:2206.03992},
  eprint = {2206.03992},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative modelling, we propose Neural Diffusion Processes (NDPs), a novel approach that learns to sample from a rich distribution over functions through its finite marginals. By introducing a custom attention block we are able to incorporate properties of stochastic processes, such as exchangeability, directly into the NDP's architecture. We empirically show that NDPs can capture functional distributions close to the true Bayesian posterior, demonstrating that they can successfully emulate the behaviour of Gaussian processes and surpass the performance of neural processes. NDPs enable a variety of downstream tasks, including regression, implicit hyperparameter marginalisation, non-Gaussian posterior prediction and global optimisation.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Neural Process\\Dutordoir_et_al-Neural_Diffusion_Processes_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\KDEKKJ6J\\2206.html}
}

@misc{dutordoir2023a,
  title = {Neural {{Diffusion Processes}}},
	author = {Dutordoir, Vincent and Saul, Alan and Ghahramani, Zoubin and Simpson, Fergus},
  year = {2023},
  number = {arXiv:2206.03992},
  eprint = {2206.03992},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2024-02-21},
  abstract = {Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative modelling, we propose Neural Diffusion Processes (NDPs), a novel approach that learns to sample from a rich distribution over functions through its finite marginals. By introducing a custom attention block we are able to incorporate properties of stochastic processes, such as exchangeability, directly into the NDP's architecture. We empirically show that NDPs can capture functional distributions close to the true Bayesian posterior, demonstrating that they can successfully emulate the behaviour of Gaussian processes and surpass the performance of neural processes. NDPs enable a variety of downstream tasks, including regression, implicit hyperparameter marginalisation, non-Gaussian posterior prediction and global optimisation.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\CJ4YJHVH\Dutordoir et al. - 2023 - Neural Diffusion Processes.pdf}
}

@phdthesis{duvenaud2014,
  title = {Automatic {{Model Construction}}  with {{Gaussian Processes}}},
	author = {Duvenaud, David Kristjanson},
  year = {2014},
  langid = {english},
  school = {University of Cambridge},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Duvenaud-Automatic_Model_Construction_with_Gaussian_Processes_2014.pdf}
}

@article{eason2014,
  title = {Adaptive Sequential Sampling for Surrogate Model Generation with Artificial Neural Networks},
	author = {Eason, John and Cremaschi, Selen},
  year = {2014},
  journal = {Computers \& Chemical Engineering},
  volume = {68},
  pages = {220--232},
  urldate = {2022-01-02},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Eason_Cremaschi-Adaptive_sequential_sampling_for_surrogate_model_generation_with_artificial_2014.pdf}
}

@article{eason2014a,
  title = {Adaptive Sequential Sampling for Surrogate Model Generation with Artificial Neural Networks},
	author = {Eason, John and Cremaschi, Selen},
  year = {2014},
  journal = {Computers \& Chemical Engineering},
  volume = {68},
  pages = {220--232},
  urldate = {2022-02-04},
  langid = {english}
}

@article{easterling2002,
  title = {Statistical {{Foundations}} for the {{Validation}} of {{Computer Models}}},
	author = {Easterling, Robert G and Berger, James O},
  year = {2002},
  pages = {28},
  abstract = {Confidence in computational predictions is enhanced if the potential `error' in these predictions (the difference between the prediction and nature's outcome in the situation being simulated) can be credibly bounded. The ``model-validation'' process by which experimental or field results are compared to computational predictions to produce this confidence provides the raw material for characterizing a computational model's predictive capability in terms of such error limits. In general, the goal is to evaluate predictive capability, first for predictions in the region of experimentation, then, if possible, for predictions in untested regions of applications. This whole process is fundamentally statistical because it requires the acquisition and careful analysis of appropriate data. We establish a statistical model for characterizing predictive-capability and discuss various experimental design and statistical data analysis issues and approaches for resolving them Analyses based on both `frequentist' and Bayesian statistical paradigms are discussed in general in this paper and illustrated in accompanying papers presented at this workshop.},
  langid = {english},
  keywords = {Framework,Frequentist,Model Validation},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Frameworks\Easterling_Berger-Statistical_Foundations_for_the_Validation_of_Computer_Models_2002.pdf}
}

@article{eca2022,
  title = {On the {{Failure}} of the {{Area Metric}} for {{Validation Exercises}} of {{Stochastic Simulations}}},
	author = {E{\c c}a, L. and Dowding, K. and Roache, P. J.},
  year = {2022},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {7},
  number = {4},
  pages = {041005},
  urldate = {2023-09-22},
  abstract = {Abstract             This paper discusses the application of the area metric to the quantification of modeling errors. The focus of the discussion is the effect of the shape of the two distributions on the result produced by the Area Metric. Two different examples that assume negligible experimental and numerical errors are presented: the first case has experimental and simulated quantities of interest defined by normal distributions that require the definition of a mean value and a standard deviation; the second example is taken from the V\&V10.1 ASME standard that applies the Area Metric to quantify the modeling error of the tip deflection of a loaded hollow tapered cantilever beam simulated with the static Bernoulli--Euler beam theory. The first example shows that relatively small differences between the mean values are sufficient for the area metric to be insensitive to the standard deviation. Furthermore, the example of the V\&V10.1 ASME standard produces an Area Metric equal to the difference between the mean values of experiments and simulations. Therefore, the error quantification is reduced to a single number that is obtained from a simple difference of two mean values. This means that the area metric fails to reflect a dependence on the difference in the shape of the distributions representing variability. The paper also presents an alternative version of the Area Metric that avoids this filtering effect of the shape of the distributions by utilizing a reference simulation that has the same mean value as the experiments. This means that the quantification of the modeling error will have contributions from the difference in mean values and the shape of the distributions.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Eca_et_al-On_the_Failure_of_the_Area_Metric_for_Validation_Exercises_of_Stochastic_2022.pdf}
}

@article{echard2011,
  title = {{{AK-MCS}}: {{An}} Active Learning Reliability Method Combining {{Kriging}} and {{Monte Carlo Simulation}}},
  shorttitle = {{{AK-MCS}}},
	author = {Echard, B. and Gayton, N. and Lemaire, M.},
  year = {2011},
  journal = {Structural Safety},
  volume = {33},
  number = {2},
  pages = {145--154},
  urldate = {2023-09-22},
  abstract = {An important challenge in structural reliability is to keep to a minimum the number of calls to the numerical models. Engineering problems involve more and more complex computer codes and the evaluation of the probability of failure may require very time-consuming computations. Metamodels are used to reduce these computation times. To assess reliability, the most popular approach remains the numerous variants of response surfaces. Polynomial Chaos [1] and Support Vector Machine [2] are also possibilities and have gained considerations among researchers in the last decades. However, recently, Kriging, originated from geostatistics, have emerged in reliability analysis. Widespread in optimisation, Kriging has just started to appear in uncertainty propagation [3] and reliability [4], [5] studies. It presents interesting characteristics such as exact interpolation and a local index of uncertainty on the prediction which can be used in active learning methods. The aim of this paper is to propose an iterative approach based on Monte Carlo Simulation and Kriging metamodel to assess the reliability of structures in a more efficient way. The method is called AK-MCS for Active learning reliability method combining Kriging and Monte Carlo Simulation. It is shown to be very efficient as the probability of failure obtained with AK-MCS is very accurate and this, for only a small number of calls to the performance function. Several examples from literature are performed to illustrate the methodology and to prove its efficiency particularly for problems dealing with high non-linearity, non-differentiability, non-convex and non-connex domains of failure and high dimensionality.},
  keywords = {Active learning,Failure probability,Kriging,Metamodel,Monte Carlo,Reliability},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Reliability Analysis\\Echard_et_al-AK-MCS_2011.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\QDJED6ZV\\S0167473011000038.html}
}

@article{echard2013,
  title = {A Combined {{Importance Sampling}} and {{Kriging}} Reliability Method for Small Failure Probabilities with Time-Demanding Numerical Models},
	author = {Echard, B. and Gayton, N. and Lemaire, M. and Relun, N.},
  year = {2013},
  journal = {Reliability Engineering \& System Safety},
  volume = {111},
  pages = {232--240},
  urldate = {2023-10-29},
  abstract = {Applying reliability methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable method called AK-IS for active learning and Kriging-based Importance Sampling. This new method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145--54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the method is, first, proved on two academic applications. It is then conducted for assessing the reliability of a challenging aerospace case study submitted to fatigue.},
  keywords = {Importance sampling,Kriging metamodel,Reliability,Small failure probability,Surrogate model},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Reliability Analysis\\Echard_et_al-A_combined_Importance_Sampling_and_Kriging_reliability_method_for_small_failure_2013.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\3LDBZ7LR\\S0951832012002086.html}
}

@article{faes2020,
  title = {Recent {{Trends}} in the {{Modeling}} and {{Quantification}} of {{Non-probabilistic Uncertainty}}},
	author = {Faes, Matthias and Moens, David},
  year = {2020},
  journal = {Archives of Computational Methods in Engineering},
  volume = {27},
  number = {3},
  pages = {633--671},
  urldate = {2023-02-04},
  abstract = {This paper gives an overview of recent advances in the field of non-probabilistic uncertainty quantification. Both techniques for the forward propagation and inverse quantification of interval and fuzzy uncertainty are discussed. Also the modeling of spatial uncertainty in an interval and fuzzy context is discussed. An in depth discussion of a recently introduced method for the inverse quantification of spatial interval uncertainty is provided and its performance is illustrated using a case studies taken from literature. It is shown that the method enables an accurate quantification of spatial uncertainty under very low data availability and with a very limited amount of assumptions on the underlying uncertainty. Finally, also a conceptual comparison with the class of Bayesian methods for uncertainty quantification is provided.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Active Learning\Faes_Moens-Recent_Trends_in_the_Modeling_and_Quantification_of_Non-probabilistic_2020.pdf}
}

@article{fang2019,
  title = {An Adaptive Sequential Experiment Design Method for Model Validation},
	author = {Fang, Ke and Zhou, Yuchen and Ma, Ping},
  year = {2019},
  journal = {Chinese Journal of Aeronautics},
  volume = {33},
  number = {6},
  pages = {1661--1672},
  urldate = {2021-09-07},
  abstract = {Efficient experiment design is of great significance for the validation of simulation model with high nonlinearity and large input space. Excessive validation experiment raises the cost while insufficient test increases the risks of accepting an invalid model. In this paper, an adaptive sequential experiment design method combining global exploration criterion and local exploitation criterion is proposed. The exploration criterion utilizes discrepancy metric to improve the space-filling property of the design points while the exploitation criterion employs the leave one out error to discover informative points. To avoid the clustering of samples in the local region, an adaptive weight updating approach is provided to maintain the balance between exploration and exploitation. Besides, the credibility distribution function characterizing the relationship between the input and result credibility is introduced to support the model validation experiment design. Finally, six benchmark problems and an engineering case are applied to examine the performance of the proposed method. The experiments indicate that the proposed method achieves satisfactory performance for function approximation in accuracy and convergence.},
  langid = {english},
  keywords = {Adaptive Sampling,Design of Experiments,Efficient Model Validation,Gaussian processes,Latin Hypercube Sampling,Metamodeling,Model Validation,To Implement},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Efficient Model Validation\Fang_et_al-An_adaptive_sequential_experiment_design_method_for_model_validation_2019.pdf}
}

@article{fannjiang2022,
  title = {Conformal Prediction for the Design Problem},
	author = {Fannjiang, Clara and Bates, Stephen and Angelopoulos, Anastasios N. and Listgarten, Jennifer and Jordan, Michael I.},
  year = {2022},
  journal = {Proceedings of the National Academy of Sciences},
  volume = {119},
  number = {43},
  eprint = {2202.03613},
  primaryclass = {cs, q-bio, stat},
  pages = {e2204569119},
  urldate = {2024-03-05},
  abstract = {Many applications of machine learning methods involve an iterative protocol in which data are collected, a model is trained, and then outputs of that model are used to choose what data to consider next. For example, one data-driven approach for designing proteins is to train a regression model to predict the fitness of protein sequences, then use it to propose new sequences believed to exhibit greater fitness than observed in the training data. Since validating designed sequences in the wet lab is typically costly, it is important to quantify the uncertainty in the model's predictions. This is challenging because of a characteristic type of distribution shift between the training and test data in the design setting -- one in which the training and test data are statistically dependent, as the latter is chosen based on the former. Consequently, the model's error on the test data -- that is, the designed sequences -- has an unknown and possibly complex relationship with its error on the training data. We introduce a method to quantify predictive uncertainty in such settings. We do so by constructing confidence sets for predictions that account for the dependence between the training and test data. The confidence sets we construct have finite-sample guarantees that hold for any prediction algorithm, even when a trained model chooses the test-time input distribution. As a motivating use case, we demonstrate with several real data sets how our method quantifies uncertainty for the predicted fitness of designed proteins, and can therefore be used to select design algorithms that achieve acceptable trade-offs between high predicted fitness and low predictive uncertainty.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Quantitative Biology - Quantitative Methods,Statistics - Methodology},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Conformal Prediction\\Fannjiang_et_al-Conformal_prediction_for_the_design_problem_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\KJ93DU3E\\2202.html}
}

@misc{farquhar2021,
  title = {On {{Statistical Bias In Active Learning}}: {{How}} and {{When To Fix It}}},
  shorttitle = {On {{Statistical Bias In Active Learning}}},
	author = {Farquhar, Sebastian and Gal, Yarin and Rainforth, Tom},
  year = {2021},
  number = {arXiv:2101.11665},
  eprint = {2101.11665},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {Active learning is a powerful tool when labelling data is expensive, but it introduces a bias because the training data no longer follows the population distribution. We formalize this bias and investigate the situations in which it can be harmful and sometimes even helpful. We further introduce novel corrective weights to remove bias when doing so is beneficial. Through this, our work not only provides a useful mechanism that can improve the active learning approach, but also an explanation of the empirical successes of various existing approaches which ignore this bias. In particular, we show that this bias can be actively helpful when training overparameterized models -- like neural networks -- with relatively little data.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Active Learning\\Farquhar_et_al-On_Statistical_Bias_In_Active_Learning_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\EYU2FXJ5\\2101.html}
}

@article{feldmann2022,
  title = {A {{Methodology}} for the {{Efficient Quantification}} of {{Parameter}} and {{Model Uncertainty}}},
	author = {Feldmann, R. and Gehb, C. M. and Schaeffner, M. and Melz, T.},
  year = {2022},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {7},
  number = {031001},
  urldate = {2023-09-22},
  abstract = {Complex structural systems often entail computationally intensive models that require efficient methods for statistical model calibration due to the high number of required model evaluations. In this paper, we present a Bayesian inference-based methodology for efficient statistical model calibration that builds upon the combination of the speed in the computation of a low-fidelity model with the accuracy of the computationally intensive high-fidelity model. The proposed two-stage method incorporates the adaptive Metropolis algorithm and a Gaussian process (GP)-based adaptive surrogate model as a low-fidelity model. In order to account for model uncertainty, we incorporate a GP-based discrepancy function into the model calibration. By calibrating the hyperparameters of the discrepancy function alongside the model parameters, we prevent the results of the model calibration to be biased. The methodology is illustrated by the statistical model calibration of a damping parameter in the modular active spring-damper system, a structural system developed within the collaborative research center SFB 805 at the Technical University of Darmstadt. The reduction of parameter and model uncertainty achieved by the application of our methodology is quantified and illustrated by assessing the predictive capability of the mathematical model of the modular active spring-damper system.},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\Feldmann_et_al-A_Methodology_for_the_Efficient_Quantification_of_Parameter_and_Model_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\DUZ5N7US\\A-Methodology-for-the-Efficient-Quantification-of.html}
}

@article{ferson2008,
  title = {Model Validation and Predictive Capability for the Thermal Challenge Problem},
	author = {Ferson, Scott and Oberkampf, William L. and Ginzburg, Lev},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2408--2430},
  urldate = {2021-09-07},
  abstract = {We address the thermal problem posed at the Sandia Validation Challenge Workshop. Unlike traditional approaches that confound calibration with validation and prediction, our approach strictly distinguishes these activities, and produces a quantitative measure of model-form uncertainty in the face of available data. We introduce a general validation metric that can be used to characterize the disagreement between the quantitative predictions from a model and relevant empirical data when either or both predictions and data are expressed as probability distributions. By considering entire distributions, this approach generalizes traditional approaches to validation that focus only on the mean behaviors of predictions and observations. The proposed metric has several desirable properties that should make it practically useful in engineering, including objectiveness and robustness, retaining the units of the data themselves, and generalizing the deterministic difference. The metric can be used to assess the overall performance of a model against all the experimental observations in the validation domain and it can be extrapolated to express predictive capability of the model under conditions for which direct experimental observations are not available. We apply the metric and the scheme for characterizing predictive capability to the thermal problem.},
  langid = {english},
  keywords = {Area Metric,Bootstrap,Model Validation,Regression,Sandia Workshop,U-Pooling,Validation Metric},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\ValidationWS Sandia Lab\Ferson_et_al-Model_validation_and_predictive_capability_for_the_thermal_challenge_problem_2008.pdf}
}

@article{forrester2006,
  title = {Optimization Using {{Surrogate Models}} and Partially Converged {{Computational Fluid Dynamics Simulations}}},
	author = {Forrester, Alexander I.J and Bressloff, Neil W and Keane, Andy J},
  year = {2006},
  journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  volume = {462},
  number = {2071},
  pages = {2177--2204},
  urldate = {2022-03-22},
  abstract = {Efficient methods for global aerodynamic optimization using computational fluid dynamics simulations should aim to reduce both the time taken to evaluate design concepts and the number of evaluations needed for optimization. This paper investigates methods for improving such efficiency through the use of partially converged computational fluid dynamics results. These allow surrogate models to be built in a fraction of the time required for models based on converged results. The proposed optimization methodologies increase the speed of convergence to a global optimum while the computer resources expended in areas of poor designs are reduced. A strategy which combines a global approximation built using partially converged simulations with expected improvement updates of converged simulations is shown to outperform a traditional surrogate-based optimization.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Engineering Applications\Forrester_et_al-Optimization_using_Surrogate_Models_and_partially_converged_Computational_Fluid_2006.pdf}
}

@book{forrester2008,
  title = {Engineering {{Design}} via {{Surrogate Modelling}}: {{A Practical Guide}}},
  shorttitle = {Engineering {{Design}} via {{Surrogate Modelling}}},
	author = {Forrester, Alexander and Sobester, Andr{\'a}s and Keane, Andy},
  year = {2008},
  publisher = {John Wiley \& Sons},
  abstract = {Surrogate models expedite the search for promising designs by standing in for expensive design evaluations or simulations. They provide a global model of some metric of a design (such as weight, aerodynamic drag, cost, etc.), which can then be optimized efficiently. Engineering Design via Surrogate Modelling is a self-contained guide to surrogate models and their use in engineering design. The fundamentals of building, selecting, validating, searching and refining a surrogate are presented in a manner accessible to novices in the field. Figures are used liberally to explain the key concepts and clearly show the differences between the various techniques, as well as to emphasize the intuitive nature of the conceptual and mathematical reasoning behind them. More advanced and recent concepts are each presented in stand-alone chapters, allowing the reader to concentrate on material pertinent to their current design problem, and concepts are clearly demonstrated using simple design problems. This collection of advanced concepts (visualization, constraint handling, coping with noisy data, gradient-enhanced modelling, multi-fidelity analysis and multiple objectives) represents an invaluable reference manual for engineers and researchers active in the area. Engineering Design via Surrogate Modelling is complemented by a suite of Matlab codes, allowing the reader to apply all the techniques presented to their own design problems. By applying statistical modelling to engineering design, this book bridges the wide gap between the engineering and statistics communities. It will appeal to postgraduates and researchers across the academic engineering design community as well as practising design engineers.  Provides an inclusive and practical guide to using surrogates in engineering design. Presents the fundamentals of building, selecting, validating, searching and refining a surrogate model. Guides the reader through the practical implementation of a surrogate-based design process using a set of case studies from real engineering design challenges.  Accompanied by a companion website featuring Matlab software at http://www.wiley.com/go/forrester},
  langid = {english},
  keywords = {Technology & Engineering / Drafting & Mechanical Drawing,Technology & Engineering / Manufacturing,Technology & Engineering / Mechanical}
}

@misc{fortuin2020,
  title = {{{GP-VAE}}: {{Deep Probabilistic Time Series Imputation}}},
  shorttitle = {{{GP-VAE}}},
	author = {Fortuin, Vincent and Baranchuk, Dmitry and R{\"a}tsch, Gunnar and Mandt, Stephan},
  year = {2020},
  number = {arXiv:1907.04155},
  eprint = {1907.04155},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-10-19},
  abstract = {Multivariate time series with missing values are common in areas such as healthcare and finance, and have grown in number and complexity over the years. This raises the question whether deep learning methodologies can outperform classical data imputation methods in this domain. However, naive applications of deep learning fall short in giving reliable confidence estimates and lack interpretability. We propose a new deep sequential latent variable model for dimensionality reduction and data imputation. Our modeling assumption is simple and interpretable: the high dimensional time series has a lower-dimensional representation which evolves smoothly in time according to a Gaussian process. The non-linear dimensionality reduction in the presence of missing data is achieved using a VAE approach with a novel structured variational approximation. We demonstrate that our approach outperforms several classical and deep learning-based data imputation methods on high-dimensional data from the domains of computer vision and healthcare, while additionally improving the smoothness of the imputations and providing interpretable uncertainty estimates.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Fortuin_et_al-GP-VAE_2020.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\DN8NXBI6\\1907.html}
}

@article{fortuin2021,
  title = {Bayesian {{Neural Network Priors Revisited}}},
	author = {Fortuin, Vincent and {Garriga-Alonso}, Adri{\`a} and Wenzel, Florian and R{\"a}tsch, Gunnar and Turner, Richard and others},
  year = {2021},
  journal = {arXiv:2102.06571},
  eprint = {2102.06571},
  urldate = {2022-01-21},
  abstract = {Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, it is unclear whether these priors accurately reflect our true beliefs about the weight distributions or give optimal performance. To find better priors, we study summary statistics of neural network weights in networks trained using SGD. We find that convolutional neural network (CNN) weights display strong spatial correlations, while fully connected networks (FCNNs) display heavy-tailed weight distributions. Building these observations into priors leads to improved performance on a variety of image classification datasets. Surprisingly, these priors mitigate the cold posterior effect in FCNNs, but slightly increase the cold posterior effect in ResNets.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Bayesian Neural Networks\Fortuin_et_al-Bayesian_Neural_Network_Priors_Revisited_2021.pdf}
}

@misc{foster2020,
  title = {Variational {{Bayesian Optimal Experimental Design}}},
	author = {Foster, Adam and Jankowiak, Martin and Bingham, Eli and Horsfall, Paul and Teh, Yee Whye and others},
  year = {2020},
  number = {arXiv:1903.05480},
  eprint = {1903.05480},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information gain (EIG) of an experiment. To address this, we introduce several classes of fast EIG estimators by building on ideas from amortized variational inference. We show theoretically and empirically that these estimators can provide significant gains in speed and accuracy over previous approaches. We further demonstrate the practicality of our approach on a number of end-to-end experiments.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Computation,Statistics - Machine Learning,Statistics - Methodology},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Design of Experiments\\Foster_et_al-Variational_Bayesian_Optimal_Experimental_Design_2020.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\BA9MY9TH\\1903.html}
}

@misc{foster2021,
  title = {Deep {{Adaptive Design}}: {{Amortizing Sequential Bayesian Experimental Design}}},
  shorttitle = {Deep {{Adaptive Design}}},
	author = {Foster, Adam and Ivanova, Desi R. and Malik, Ilyas and Rainforth, Tom},
  year = {2021},
  number = {arXiv:2103.02438},
  eprint = {2103.02438},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {We introduce Deep Adaptive Design (DAD), a method for amortizing the cost of adaptive Bayesian experimental design that allows experiments to be run in real-time. Traditional sequential Bayesian optimal experimental design approaches require substantial computation at each stage of the experiment. This makes them unsuitable for most real-world applications, where decisions must typically be made quickly. DAD addresses this restriction by learning an amortized design network upfront and then using this to rapidly run (multiple) adaptive experiments at deployment time. This network represents a design policy which takes as input the data from previous steps, and outputs the next design using a single forward pass; these design decisions can be made in milliseconds during the live experiment. To train the network, we introduce contrastive information bounds that are suitable objectives for the sequential setting, and propose a customized network architecture that exploits key symmetries. We demonstrate that DAD successfully amortizes the process of experimental design, outperforming alternative strategies on a number of problems.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning,Statistics - Computation,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Design of Experiments\\Adaptive Methods\\Foster_et_al-Deep_Adaptive_Design_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\3R4A4QYF\\2103.html}
}

@inproceedings{foster2021a,
  title = {Deep {{Adaptive Design}}: {{Amortizing Sequential Bayesian Experimental Design}}},
  shorttitle = {Deep {{Adaptive Design}}},
  booktitle = {Proceedings of the 38th {{International Conference}} on {{Machine Learning}}},
	author = {Foster, Adam and Ivanova, Desi R. and Malik, Ilyas and Rainforth, Tom},
  year = {2021},
  pages = {3384--3395},
  publisher = {PMLR},
  urldate = {2023-07-19},
  abstract = {We introduce Deep Adaptive Design (DAD), a method for amortizing the cost of adaptive Bayesian experimental design that allows experiments to be run in real-time. Traditional sequential Bayesian optimal experimental design approaches require substantial computation at each stage of the experiment. This makes them unsuitable for most real-world applications, where decisions must typically be made quickly. DAD addresses this restriction by learning an amortized design network upfront and then using this to rapidly run (multiple) adaptive experiments at deployment time. This network represents a design policy which takes as input the data from previous steps, and outputs the next design using a single forward pass; these design decisions can be made in milliseconds during the live experiment. To train the network, we introduce contrastive information bounds that are suitable objectives for the sequential setting, and propose a customized network architecture that exploits key symmetries. We demonstrate that DAD successfully amortizes the process of experimental design, outperforming alternative strategies on a number of problems.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Bayesian Experimental Design\Foster_et_al-Deep_Adaptive_Design_2021.pdf}
}

@article{frazier2018,
  title = {A {{Tutorial}} on {{Bayesian Optimization}}},
	author = {Frazier, Peter I.},
  year = {2018},
  journal = {arXiv:1807.02811},
  eprint = {1807.02811},
  urldate = {2021-09-07},
  abstract = {Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Adaptive Sampling,Bayesian Optimization,Design of Experiments,Gaussian processes,Machine learning,Optimization},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Frazier-A_Tutorial_on_Bayesian_Optimization_2018.pdf}
}

@article{freno2019,
  title = {Machine-Learning Error Models for Approximate Solutions to Parameterized Systems of Nonlinear Equations},
	author = {Freno, Brian A. and Carlberg, Kevin T.},
  year = {2019},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {348},
  pages = {250--296},
  urldate = {2023-12-21},
  abstract = {This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of an iterative method, a lower-fidelity model, or a projection-based reduced-order model, for example. The proposed statistical model comprises the sum of a deterministic regression-function model and a stochastic noise model. The method constructs the regression-function model by applying regression techniques from machine learning (e.g., support vector regression, artificial neural networks) to map features (i.e., error indicators such as sampled elements of the residual) to a prediction of the approximate-solution error. The method constructs the noise model as a mean-zero Gaussian random variable whose variance is computed as the sample variance of the approximate-solution error on a test set; this variance can be interpreted as the epistemic uncertainty introduced by the approximate solution. This work considers a wide range of feature-engineering methods, data-set-construction techniques, and regression techniques that aim to ensure that (1) the features are cheaply computable, (2) the noise model exhibits low variance (i.e., low epistemic uncertainty introduced), and (3) the regression model generalizes to independent test data. Numerical experiments performed on several computational-mechanics problems and types of approximate solutions demonstrate the ability of the method to generate statistical models of the error that satisfy these criteria and significantly outperform more commonly adopted approaches for error modeling.},
  keywords = {Error modeling,High-dimensional regression,Model reduction,Parameterized nonlinear equations,ROMES method,Supervised machine learning},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Error learning\Freno_Carlberg-Machine-learning_error_models_for_approximate_solutions_to_parameterized_2019.pdf}
}

@article{fries2010,
  title = {The Extended/Generalized {{Finite Element Method}}: {{An Overview}} of the {{Method}} and Its {{Applications}}},
	author = {Fries, Thomas-Peter and Belytschko, Ted},
  year = {2010},
  journal = {International Journal for Numerical Methods in Engineering},
  volume = {84},
  number = {3},
  pages = {253--304},
  urldate = {2022-03-22},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Engineering Applications\Fries_Belytschko-The_extended-generalized_Finite_Element_Method_2010.pdf}
}

@article{fuhg2021,
  title = {State-of-the-{{Art}} and {{Comparative Review}} of {{Adaptive Sampling Methods}} for {{Kriging}}},
	author = {Fuhg, Jan N. and Fau, Am{\'e}lie and Nackenhorst, Udo},
  year = {2021},
  journal = {Archives of Computational Methods in Engineering},
  volume = {28},
  number = {4},
  pages = {2689--2747},
  urldate = {2021-09-07},
  abstract = {Metamodels aim to approximate characteristics of functions or systems from the knowledge extracted on only a finite number of samples. In recent years kriging has emerged as a widely applied metamodeling technique for resource-intensive computational experiments. However its prediction quality is highly dependent on the size and distribution of the given training points. Hence, in order to build proficient kriging models with as few samples as possible adaptive sampling strategies have gained considerable attention. These techniques aim to find pertinent points in an iterative manner based on information extracted from the current metamodel. A review of adaptive schemes for kriging proposed in the literature is presented in this article. The objective is to provide the reader with an overview of the main principles of adaptive techniques, and insightful details to pertinently employ available tools depending on the application at hand. In this context commonly applied strategies are compared with regards to their characteristics and approximation capabilities. In light of these experiments, it is found that the success of a scheme depends on the features of a specific problem and the goal of the analysis. In order to facilitate the entry into adaptive sampling a guide is provided. All experiments described herein are replicable using a provided open source toolbox.},
  langid = {english},
  keywords = {Adaptive Sampling,Bayesian Optimization,Comparison,Design of Experiments,Gaussian processes,Kriging,Optimization,Review,To Implement},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Fuhg_et_al-State-of-the-Art_and_Comparative_Review_of_Adaptive_Sampling_Methods_for_Kriging_2021.pdf}
}

@inproceedings{gal2016,
  title = {Dropout as a Bayesian Approximation: {{Representing}} Model Uncertainty in Deep Learning},
  booktitle = {Proceedings of the 33rd International Conference on Machine Learning},
	author = {Gal, Yarin and Ghahramani, Zoubin},
  year = {2016-06-20/2016-06-22},
  series = {Proceedings of Machine Learning Research},
  volume = {48},
  pages = {1050--1059},
  publisher = {PMLR},
  address = {New York, New York, USA},
  abstract = {Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs -- extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and non-linearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning.}
}

@phdthesis{gal2016a,
  title = {Uncertainty in {{Deep Learning}}},
	author = {Gal, Yarin},
  year = {2016},
  langid = {english},
  school = {University of Cambridge},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Uncertainty Quantification\Gal-Uncertainty_in_Deep_Learning_2016.pdf}
}

@inproceedings{gardner2017,
  title = {Discovering and {{Exploiting Additive Structure}} for {{Bayesian Optimization}}},
  booktitle = {Proceedings of the 20th {{International Conference}} on {{Artificial Intelligence}} and {{Statistics}}},
	author = {Gardner, Jacob and Guo, Chuan and Weinberger, Kilian and Garnett, Roman and Grosse, Roger},
  year = {2017},
  pages = {1311--1319},
  publisher = {PMLR},
  urldate = {2023-02-04},
  abstract = {Bayesian optimization has proven invaluable for black-box optimization of expensive functions. Its main limitation is its exponential complexity with respect to the dimensionality of the search space using typical kernels. Luckily, many objective functions can be decomposed into additive subproblems, which can be optimized independently. We investigate how to automatically discover such (typically unknown) additive structure while simultaneously exploiting it through Bayesian optimization. We propose an efficient algorithm based on Metropolis-Hastings sampling and demonstrate its efficacy empirically on synthetic and real-world data sets. Throughout all our experiments we reliably discover hidden additive structure whenever it exists and exploit it to yield significantly faster convergence.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Gardner_et_al-Discovering_and_Exploiting_Additive_Structure_for_Bayesian_Optimization_2017.pdf}
}

@inproceedings{gardner2017a,
  title = {Discovering and {{Exploiting Additive Structure}} for {{Bayesian Optimization}}},
  booktitle = {Proceedings of the 20th {{International Conference}} on {{Artificial Intelligence}} and {{Statistics}}},
	author = {Gardner, Jacob and Guo, Chuan and Weinberger, Kilian and Garnett, Roman and Grosse, Roger},
  year = {2017},
  pages = {1311--1319},
  publisher = {PMLR},
  urldate = {2023-02-04},
  abstract = {Bayesian optimization has proven invaluable for black-box optimization of expensive functions. Its main limitation is its exponential complexity with respect to the dimensionality of the search space using typical kernels. Luckily, many objective functions can be decomposed into additive subproblems, which can be optimized independently. We investigate how to automatically discover such (typically unknown) additive structure while simultaneously exploiting it through Bayesian optimization. We propose an efficient algorithm based on Metropolis-Hastings sampling and demonstrate its efficacy empirically on synthetic and real-world data sets. Throughout all our experiments we reliably discover hidden additive structure whenever it exists and exploit it to yield significantly faster convergence.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Active Learning\Gardner_et_al-Discovering_and_Exploiting_Additive_Structure_for_Bayesian_Optimization_2017.pdf}
}

@inproceedings{gardner2018,
  title = {{{GPyTorch}}: {{Blackbox Matrix-Matrix Gaussian Process Inference}} with {{GPU Acceleration}}},
  shorttitle = {{{GPyTorch}}},
  booktitle = {Advances in {{Neural Information Processing Systems}}},
	author = {Gardner, Jacob and Pleiss, Geoff and Weinberger, Kilian Q and Bindel, David and Wilson, Andrew G},
  year = {2018},
  volume = {31},
  publisher = {Curran Associates, Inc.},
  urldate = {2024-01-31},
  abstract = {Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched version of the conjugate gradients algorithm to derive all terms for training and inference in a single call. BBMM reduces the asymptotic complexity of exact GP inference from O(n{\textasciicircum}3) to O(n{\textasciicircum}2). Adapting this algorithm to scalable approximations and complex GP models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM uses a specialized preconditioner to substantially speed up convergence. In experiments we show that BBMM effectively uses GPU hardware to dramatically accelerate both exact GP inference and scalable approximations. Additionally, we provide GPyTorch, a software platform for scalable GP inference via BBMM, built on PyTorch.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Software_Packages\Gardner_et_al-GPyTorch_2018.pdf}
}

@article{gardner2019,
  title = {A {{Unifying Framework}} for {{Probabilistic Validation Metrics}}},
	author = {Gardner, Paul and Lord, Charles and Barthorpe, Robert J.},
  year = {2019},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {4},
  number = {3},
  pages = {031005},
  urldate = {2021-09-07},
  abstract = {Abstract             Probabilistic modeling methods are increasingly being employed in engineering applications. These approaches make inferences about the distribution for output quantities of interest. A challenge in applying probabilistic computer models (simulators) is validating output distributions against samples from observational data. An ideal validation metric is one that intuitively provides information on key differences between the simulator output and observational distributions, such as statistical distances/divergences. Within the literature, only a small set of statistical distances/divergences have been utilized for this task; often selected based on user experience and without reference to the wider variety available. As a result, this paper offers a unifying framework of statistical distances/divergences, categorizing those implemented within the literature, providing a greater understanding of their benefits, and offering new potential measures as validation metrics. In this paper, two families of measures for quantifying differences between distributions, that encompass the existing statistical distances/divergences within the literature, are analyzed: f-divergence and integral probability metrics (IPMs). Specific measures from these families are highlighted, providing an assessment of current and new validation metrics, with a discussion of their merits in determining simulator adequacy, offering validation metrics with greater sensitivity in quantifying differences across the range of probability mass.},
  langid = {english},
  keywords = {Model Validation,Validation Metric},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Gardner_et_al-A_Unifying_Framework_for_Probabilistic_Validation_Metrics_2019.pdf}
}

@article{gardner2021,
  title = {Learning Model Discrepancy: {{A Gaussian}} Process and Sampling-Based Approach},
  shorttitle = {Learning Model Discrepancy},
	author = {Gardner, P. and Rogers, T. J. and Lord, C. and Barthorpe, R. J.},
  year = {2021},
  journal = {Mechanical Systems and Signal Processing},
  volume = {152},
  pages = {107381},
  urldate = {2023-05-10},
  abstract = {Predicting events in the real world with a computer model (simulator) is challenging. Every simulator, to varying extents, has model discrepancy, a mismatch between real world observations and the simulator (given the `true' parameters are known). Model discrepancy occurs for various reasons, including simplified or missing physics in the simulator, numerical approximations that are required to compute the simulator outputs, and the fact that assumptions in the simulator are not generally applicable to all real world contexts. The existence of model discrepancy is problematic for the engineer as performing calibration of the simulator will lead to biased parameter estimates, and the resulting simulator is unlikely to accurately predict (or even be valid for) various contexts of interest. This paper proposes an approach for inferring model discrepancy that overcomes non-identifiability problems associated with jointly inferring the simulator parameters along with the model discrepancy. Instead, the proposed procedure seeks to identify model discrepancy given some parameter distribution, which could come from a `likelihood-free' approach that considers the presence of model discrepancy during calibration, such as Bayesian history matching. In this case, model discrepancy is inferred whilst marginalising out the uncertain simulator outputs via a sampling-based approach, therefore better reflecting the `true' uncertainty associated with the model discrepancy. Verification of the approach is performed before a demonstration on an experiential case study, comprising a representative five storey building structure.},
  langid = {english},
  keywords = {Bayesian history matching,Gaussian process regression,Importance sampling,Model discrepancy},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\DBC\\KOH\\Gardner_et_al-Learning_model_discrepancy_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\D4RYB5RZ\\S0888327020307676.html}
}

@misc{garnelo2018,
  title = {Neural {{Processes}}},
	author = {Garnelo, Marta and Schwarz, Jonathan and Rosenbaum, Dan and Viola, Fabio and Rezende, Danilo J. and others},
  year = {2018},
  number = {arXiv:1807.01622},
  eprint = {1807.01622},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {A neural network (NN) is a parameterised function that can be tuned via gradient descent to approximate a labelled collection of data with high precision. A Gaussian process (GP), on the other hand, is a probabilistic model that defines a distribution over possible functions, and is updated in light of data via the rules of probabilistic inference. GPs are probabilistic, data-efficient and flexible, however they are also computationally intensive and thus limited in their applicability. We introduce a class of neural latent variable models which we call Neural Processes (NPs), combining the best of both worlds. Like GPs, NPs define distributions over functions, are capable of rapid adaptation to new observations, and can estimate the uncertainty in their predictions. Like NNs, NPs are computationally efficient during training and evaluation but also learn to adapt their priors to data. We demonstrate the performance of NPs on a range of learning tasks, including regression and optimisation, and compare and contrast with related models in the literature.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Neural Process\\Garnelo_et_al-Neural_Processes_2018.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\D3V2N56J\\1807.html}
}

@misc{garnelo2018a,
  title = {Conditional {{Neural Processes}}},
	author = {Garnelo, Marta and Rosenbaum, Dan and Maddison, Chris J. and Ramalho, Tiago and Saxton, David and others},
  year = {2018},
  number = {arXiv:1807.01613},
  eprint = {1807.01613},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {Deep neural networks excel at function approximation, yet they are typically trained from scratch for each new function. On the other hand, Bayesian methods, such as Gaussian Processes (GPs), exploit prior knowledge to quickly infer the shape of a new function at test time. Yet GPs are computationally expensive, and it can be hard to design appropriate priors. In this paper we propose a family of neural models, Conditional Neural Processes (CNPs), that combine the benefits of both. CNPs are inspired by the flexibility of stochastic processes such as GPs, but are structured as neural networks and trained via gradient descent. CNPs make accurate predictions after observing only a handful of training data points, yet scale to complex functions and large datasets. We demonstrate the performance and versatility of the approach on a range of canonical machine learning tasks, including regression, classification and image completion.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Neural Process\\Garnelo_et_al-Conditional_Neural_Processes_2018.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\E6TDA45G\\1807.html}
}

@book{garnett2022,
  title = {Bayesian {{Optimization}}},
	author = {Garnett, Roman},
  year = {2022},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Garnett-Bayesian_Optimization_2022.pdf}
}

@book{ghosh2006,
  title = {An Introduction to {{Bayesian}} Analysis: Theory and Methods},
  shorttitle = {An Introduction to {{Bayesian}} Analysis},
	author = {Ghosh, J. K. and Delampady, Mohan and Samanta, Tapas},
  year = {2006},
  series = {Springer Texts in Statistics},
  publisher = {Springer},
  address = {New York},
  langid = {english},
  lccn = {QA279.5 .G483 2006},
  keywords = {Bayesian statistical decision theory},
  annotation = {OCLC: ocm71298494},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\9YRHE5SU\Ghosh et al. - 2006 - An introduction to Bayesian analysis theory and m.pdf}
}

@article{girard2003,
  title = {Learning a {{Gaussian Process Model}} with {{Uncertain Inputs}}},
	author = {Girard, Agathe and {Murray-Smith}, Roderick},
  year = {2003},
  pages = {10},
  abstract = {Learning with uncertain inputs is well-known to be a difficult task. In order to achieve this analytically using a Gaussian Process prior model, we expand the original process around the input mean (Delta method), assuming the random input is normally distributed. We thus derive a new process whose covariance function accounts for the randomness of the input. We illustrate the effectiveness of the proposed model on a simple static simulation example and on the modelling of a nonlinear noisy time-series.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Girard_Murray-Smith-Learning_a_Gaussian_Process_Model_with_Uncertain_Inputs_2003.pdf}
}

@inproceedings{goh2022,
  title = {Solving {{Bayesian Inverse Problems}} via {{Variational Autoencoders}}},
  booktitle = {Proceedings of the 2nd {{Mathematical}} and {{Scientific Machine Learning Conference}}},
	author = {Goh, Hwan and Sheriffdeen, Sheroze and Wittmer, Jonathan and {Bui-Thanh}, Tan},
  year = {2022},
  pages = {386--425},
  publisher = {PMLR},
  urldate = {2023-02-04},
  abstract = {In recent years, the field of machine learning has made phenomenal progress in the pursuit of simu- lating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a small shift in perspective, we leverage and adapt VAEs for a different purpose: uncertainty quantification (UQ) in scientific inverse problems. We intro- duce UQ-VAE: a flexible, adaptive, hybrid data/model-constrained framework for training neural networks capable of rapid modelling of the posterior distribution representing the unknown param- eter of interest. Specifically, from divergence-based variational inference, our framework is derived such that most of the information usually present in scientific inverse problems is fully utilized in the training procedure. Additionally, this framework includes an adjustable hyperparameter that allows selection of the notion of distance between the posterior model and the target distribution. This introduces more flexibility in controlling how optimization directs the learning of the posterior model. Further, this framework possesses an inherent adaptive optimization property that emerges through the learning of the posterior uncertainty. Numerical results for an elliptic PDE-constrained Bayesian inverse problem are provided to verify the proposed framework.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Goh_et_al-Solving_Bayesian_Inverse_Problems_via_Variational_Autoencoders_2022.pdf}
}

@book{goodfellow2016,
  title = {Deep Learning},
	author = {Goodfellow, Ian and Bengio, Yoshua and Courville, Aaron},
  year = {2016},
  series = {Adaptive Computation and Machine Learning},
  publisher = {The MIT Press},
  address = {Cambridge, Massachusetts},
  lccn = {Q325.5 .G66 2016},
  keywords = {Autoencoders,Basics,Classification,Deep Networks,Machine learning,Monte Carlo,Neuronal Network,Optimization,Regression,Sampling},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Goodfellow_et_al-Deep_learning_2016.pdf}
}

@inproceedings{gotovos2013,
  title = {Active Learning for Level Set Estimation},
  booktitle = {Proceedings of the {{Twenty-Third International Joint Conference}} on {{Artificial Intelligence}}},
	author = {Gotovos, Alkis and Casati, Nathalie and Hitz, Gregory and Krause, Andreas},
  year = {2013},
  series = {{{IJCAI}} '13},
  pages = {1344--1350},
  publisher = {AAAI Press},
  address = {Beijing, China},
  urldate = {2024-05-09},
}

@misc{gpy2014,
  title = {{{GPy}}: {{A Gaussian}} Process Framework in Python},
	author = {Hensman, James and Fusi, Nicolo and Andrade, Ricardo and Durrande, Nicolas and Saul, Alan and others},
  year = {2014}
}

@article{gramacy2010,
  title = {Cases for the Nugget in Modeling Computer Experiments},
	author = {Gramacy, Robert B. and Lee, Herbert K. H.},
  year = {2010},
  journal = {arXiv:1007.4580},
  eprint = {1007.4580},
  urldate = {2022-01-20},
  abstract = {Most surrogate models for computer experiments are interpolators, and the most common interpolator is a Gaussian process (GP) that deliberately omits a small-scale (measurement) error term called the nugget. The explanation is that computer experiments are, by definition, "deterministic", and so there is no measurement error. We think this is too narrow a focus for a computer experiment and a statistically inefficient way to model them. We show that estimating a (non-zero) nugget can lead to surrogate models with better statistical properties, such as predictive accuracy and coverage, in a variety of common situations.},
  archiveprefix = {arxiv},
  keywords = {Statistics - Computation}
}

@article{greenhill2020,
  title = {Bayesian {{Optimization}} for {{Adaptive Experimental Design}}: {{A Review}}},
  shorttitle = {Bayesian {{Optimization}} for {{Adaptive Experimental Design}}},
	author = {Greenhill, Stewart and Rana, Santu and Gupta, Sunil and Vellanki, Pratibha and Venkatesh, Svetha},
  year = {2020},
  journal = {IEEE Access},
  volume = {8},
  pages = {13937--13948},
  urldate = {2021-09-07},
  abstract = {Bayesian optimisation is a statistical method that efficiently models and optimises expensive ``black-box'' functions. This review considers the application of Bayesian optimisation to experimental design, in comparison to existing Design of Experiments (DOE) methods. Solutions are surveyed for a range of core issues in experimental design including: the incorporation of prior knowledge, high dimensional optimisation, constraints, batch evaluation, multiple objectives, multi-fidelity data, and mixed variable types.},
  langid = {english},
  keywords = {Adaptive Sampling,Bayesian Optimization,Design of Experiments,Gaussian processes,Kriging,Optimization},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Greenhill_et_al-Bayesian_Optimization_for_Adaptive_Experimental_Design_2020.pdf}
}

@article{gretton2012,
  title = {A {{Kernel Two-Sample Test}}},
	author = {Gretton, Arthur and Borgwardt, Karsten M. and Rasch, Malte J. and Schoelkopf, Bernhard and Smola, Alexander},
  year = {2012},
  journal = {Journal of Machine Learning Research},
  volume = {13},
  pages = {723--773},
  abstract = {We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD).We present two distributionfree tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.},
  langid = {english},
  keywords = {Hypothesis Testing,Kernel Methods,Model Validation,Statistics,Validation Metric},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Gretton_et_al-A_Kernel_Two-Sample_Test_2012.pdf}
}

@article{gu2021,
  title = {{{SelectNet}}: {{Self-paced}} Learning for High-Dimensional Partial Differential Equations},
  shorttitle = {{{SelectNet}}},
	author = {Gu, Yiqi and Yang, Haizhao and Zhou, Chao},
  year = {2021},
  journal = {Journal of Computational Physics},
  volume = {441},
  pages = {110444},
  urldate = {2023-06-15},
  abstract = {The least squares method with deep neural networks as function parametrization has been applied to solve certain high-dimensional partial differential equations (PDEs) successfully; however, its convergence is slow and might not be guaranteed even within a simple class of PDEs. To improve the convergence of the network-based least squares model, we introduce a novel self-paced learning framework, SelectNet, which quantifies the difficulty of training samples, treats samples equally in the early stage of training, and slowly explores more challenging samples, e.g., samples with larger residual errors, mimicking the human cognitive process for more efficient learning. In particular, a selection network and the PDE solution network are trained simultaneously; the selection network adaptively weighting the training samples of the solution network achieving the goal of self-paced learning. Numerical examples indicate that the proposed SelectNet model outperforms existing models on the convergence speed and the convergence robustness, especially for low-regularity solutions.},
  langid = {english},
  keywords = {Convergence,Deep neural networks,High-dimensional PDEs,Least square method,Selected sampling,Self-paced learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Design of Experiments\\Adaptive Methods\\PINN\\Gu_et_al-SelectNet_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\P5KI4WCM\\S0021999121003399.html}
}

@article{hallqvist2021,
  title = {Optimal {{Selection}} of {{Model Validation Experiments}}: {{Guided}} by {{Coverage}}},
  shorttitle = {Optimal {{Selection}} of {{Model Validation Experiments}}},
	author = {H{\"a}llqvist, Robert and Braun, Robert and Eek, Magnus and Krus, Petter},
  year = {2021},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {6},
  number = {3},
  pages = {031006},
  urldate = {2023-09-22},
  abstract = {Abstract             Modeling and Simulation (M\&S) is seen as a means to mitigate the difficulties associated with increased system complexity, integration, and cross-couplings effects encountered during development of aircraft subsystems. As a consequence, knowledge of model validity is necessary for taking robust and justified design decisions. This paper presents a method for using coverage metrics to formulate an optimal model validation strategy. Three fundamentally different and industrially relevant use-cases are presented. The first use-case entails the successive identification of validation settings, and the second considers the simultaneous identification of n validation settings. The latter of these two use-cases is finally expanded to incorporate a secondary model-based objective to the optimization problem in a third use-case. The approach presented is designed to be scalable and generic to models of industrially relevant complexity. As a result, selecting experiments for validation is done objectively with little required manual effort.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Efficient Model Validation\Hallqvist_et_al-Optimal_Selection_of_Model_Validation_Experiments_2021.pdf}
}

@article{hartman1973,
  title = {Some Experiments in Global Optimization},
	author = {Hartman, James K.},
  year = {1973},
  journal = {Naval Research Logistics Quarterly},
  volume = {20},
  number = {3},
  pages = {569--576},
  urldate = {2022-01-20},
  langid = {english}
}

@article{heckerman2021,
  title = {A {{Tutorial}} on {{Learning With Bayesian Networks}}},
	author = {Heckerman, David},
  year = {2021},
  journal = {arXiv:2002.00269},
  eprint = {2002.00269},
  urldate = {2021-09-07},
  abstract = {A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because the model encodes dependencies among all variables, it readily handles situations where some data entries are missing. Two, a Bayesian network can be used to learn causal relationships, and hence can be used to gain understanding about a problem domain and to predict the consequences of intervention. Three, because the model has both a causal and probabilistic semantics, it is an ideal representation for combining prior knowledge (which often comes in causal form) and data. Four, Bayesian statistical methods in conjunction with Bayesian networks offer an efficient and principled approach for avoiding the overfitting of data. In this paper, we discuss methods for constructing Bayesian networks from prior knowledge and summarize Bayesian statistical methods for using data to improve these models. With regard to the latter task, we describe methods for learning both the parameters and structure of a Bayesian network, including techniques for learning with incomplete data. In addition, we relate Bayesian-network methods for learning to techniques for supervised and unsupervised learning. We illustrate the graphical-modeling approach using a real-world case study.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Artificial Intelligence,Bayesian,Bayesian Network,Machine learning,Statistics},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Heckerman-A_Tutorial_on_Learning_With_Bayesian_Networks_2021.pdf}
}

@inproceedings{hensman2013,
  title = {Gaussian {{Processes}} for {{Big Data}}},
  booktitle = {Proceedings of the {{Twenty-Ninth Conference}} on {{Uncertainty}} in {{Artificial Intelligence}}},
	author = {Hensman, James and Fusi, Nicolo and Lawrence, Neil D.},
  year = {2013},
  pages = {282--290},
  publisher = {AUAI Press},
  address = {Bellevue, Washington, USA},
  urldate = {2022-09-15},
  abstract = {We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model in the necessary manner to perform variational inference. Our ap- proach is readily extended to models with non-Gaussian likelihoods and latent variable models based around Gaussian processes. We demonstrate the approach on a simple toy problem and two real world data sets.},
  langid = {english},
  keywords = {FOS: Computer and information sciences,Machine Learning (cs.LG),Machine Learning (stat.ML)},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Hensman_et_al-Gaussian_Processes_for_Big_Data_2013.pdf}
}

@misc{hensman2013a,
  title = {Gaussian {{Processes}} for {{Big Data}}},
	author = {Hensman, James and Fusi, Nicolo and Lawrence, Neil D.},
  year = {2013},
  number = {arXiv:1309.6835},
  eprint = {1309.6835},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2022-09-15},
  abstract = {We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model in the necessary manner to perform variational inference. Our ap- proach is readily extended to models with non-Gaussian likelihoods and latent variable models based around Gaussian processes. We demonstrate the approach on a simple toy problem and two real world data sets.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\EMPTY_COLLECTION_NAME\\Hensman_et_al-Gaussian_Processes_for_Big_Data_2013.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\LUVKCCSF\\1309.html}
}

@inproceedings{hensman2015,
  title = {{{MCMC}} for {{Variationally Sparse Gaussian Processes}}},
  booktitle = {Advances in {{Neural Information Processing Systems}}},
	author = {Hensman, James and Matthews, Alexander G and Filippone, Maurizio and Ghahramani, Zoubin},
  year = {2015},
  volume = {28},
  pages = {9},
  publisher = {Curran Associates, Inc.},
  abstract = {Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to approximate the posterior when the likelihood is not Gaussian and how to estimate covariance function parameter posteriors. This paper simultaneously addresses these, using a variational approximation to the posterior which is sparse in support of the function but otherwise free-form. The result is a Hybrid Monte-Carlo sampling scheme which allows for a non-Gaussian approximation over the function values and covariance parameters simultaneously, with efficient computations based on inducing-point sparse GPs. Code to replicate each experiment in this paper is available at github.com/sparseMCMC.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Hensman_et_al-MCMC_for_Variationally_Sparse_Gaussian_Processes_2015.pdf}
}

@article{higdon2004,
  title = {Combining {{Field Data}} and {{Computer Simulations}} for {{Calibration}} and {{Prediction}}},
	author = {Higdon, Dave and Kennedy, Marc and Cavendish, James C. and Cafeo, John A. and Ryne, Robert D.},
  year = {2004},
  journal = {SIAM Journal on Scientific Computing},
  volume = {26},
  number = {2},
  pages = {448--466},
  urldate = {2021-09-29},
  abstract = {We develop a statistical approach for characterizing uncertainty in predictions that are made with the aid of a computer simulation model. Typically, the computer simulation code models a physical system and requires a set of inputs---some known and specified, others unknown. A limited amount of field data from the true physical system is available to inform us about the unknown inputs and also to inform us about the uncertainty that is associated with a simulationbased prediction. The approach given here allows for the following: {$\bullet$} uncertainty regarding model inputs (i.e., calibration); {$\bullet$} accounting for uncertainty due to limitations on the number of simulations that can be carried out; {$\bullet$} discrepancy between the simulation code and the actual physical system; {$\bullet$} uncertainty in the observation process that yields the actual field data on the true physical system. The resulting analysis yields predictions and their associated uncertainties while accounting for multiple sources of uncertainty. We use a Bayesian formulation and rely on Gaussian process models to model unknown functions of the model inputs. The estimation is carried out using a Markov chain Monte Carlo method. This methodology is applied to two examples: a charged particle accelerator and a spot welding process.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Higdon_et_al-Combining_Field_Data_and_Computer_Simulations_for_Calibration_and_Prediction_2004.pdf}
}

@article{higdon2008,
  title = {A {{Bayesian}} Calibration Approach to the Thermal Problem},
	author = {Higdon, Dave and Nakhleh, Charles and Gattiker, James and Williams, Brian},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2431--2441},
  urldate = {2021-09-07},
  langid = {english},
  keywords = {Bayesian,Model Validation,Sandia Workshop},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\ValidationWS Sandia Lab\Higdon_et_al-A_Bayesian_calibration_approach_to_the_thermal_problem_2008.pdf}
}

@article{higdon2008a,
  title = {Computer {{Model Calibration Using High-Dimensional Output}}},
	author = {Higdon, Dave and Gattiker, James and Williams, Brian and Rightley, Maria},
  year = {2008},
  journal = {Journal of the American Statistical Association},
  volume = {103},
  number = {482},
  pages = {570--583},
  urldate = {2023-05-10},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\VPGGXS5Q\Higdon et al. - 2008 - Computer Model Calibration Using High-Dimensional .pdf}
}

@article{higdon2008b,
  title = {A {{Bayesian}} Calibration Approach to the Thermal Problem},
	author = {Higdon, Dave and Nakhleh, Charles and Gattiker, James and Williams, Brian},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2431--2441},
  urldate = {2023-05-10},
  abstract = {Many of the problems we work with at Los Alamos National Laboratory are similar to the thermal problem described in the tasking document. In this paper, we describe the tools and methods we have developed that utilize experimental data and detailed physics simulations for uncertainty quantification, and apply them to the thermal challenge problem. We then go on to address the regulatory question posed in the problem description. This statistical framework used here is largely based on the approach of Kennedy and O'Hagan [Kennedy, M., O'Hagan, A., Bayesian calibration of computer models (with discussion), J. Royal Stat. Soc. B 68 (2001) 425--464], but has been extended to deal with functional output of the simulation model.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\HCS4KY2W\Higdon et al. - 2008 - A Bayesian calibration approach to the thermal pro.pdf}
}

@article{hills2008,
  title = {Thermal Challenge Problem: {{Summary}}},
  shorttitle = {Thermal Challenge Problem},
	author = {Hills, R.G. and Dowding, K.J. and Swiler, L.},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2490--2495},
  urldate = {2021-09-07},
  abstract = {This paper summarizes the approaches used to address the thermal validation challenge problem. The approaches differ in their characterization of the thermal properties and uncertainty, the definitions and use of validation metrics, the use of validation experimental data to characterize or improve the model predictions, and the assessment of regulatory compliance. All approaches estimated regulatory failure with the resulting estimated probabilities varying by an order of magnitude.},
  langid = {english},
  keywords = {Model Validation,Sandia Workshop},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\ValidationWS Sandia Lab\Hills_et_al-Thermal_challenge_problem_2008.pdf}
}

@book{himmelblau1972,
  title = {Applied Nonlinear Programming},
	author = {Himmelblau, David Mautner},
  year = {1972},
  publisher = {McGraw-Hill},
  address = {New York},
  keywords = {Nonlinear programming}
}

@article{hinne2020,
  title = {A {{Conceptual Introduction}} to {{Bayesian Model Averaging}}},
	author = {Hinne, Max and Gronau, Quentin F},
  year = {2020},
  pages = {16},
  abstract = {Many statistical scenarios initially involve several candidate models that describe the data-generating process. Analysis often proceeds by first selecting the best model according to some criterion and then learning about the parameters of this selected model. Crucially, however, in this approach the parameter estimates are conditioned on the selected model, and any uncertainty about the model-selection process is ignored. An alternative is to learn the parameters for all candidate models and then combine the estimates according to the posterior probabilities of the associated models. This approach is known as Bayesian model averaging (BMA). BMA has several important advantages over all-or-none selection methods, but has been used only sparingly in the social sciences. In this conceptual introduction, we explain the principles of BMA, describe its advantages over all-or-none model selection, and showcase its utility in three examples: analysis of covariance, meta-analysis, and network analysis.},
  langid = {english}
}

@article{hinne2020a,
  title = {A {{Conceptual Introduction}} to {{Bayesian Model Averaging}}},
	author = {Hinne, Max and Gronau, Quentin F. and {van den Bergh}, Don and Wagenmakers, Eric-Jan},
  year = {2020},
  journal = {Advances in Methods and Practices in Psychological Science},
  volume = {3},
  number = {2},
  pages = {200--215},
  urldate = {2022-01-21},
  abstract = {Many statistical scenarios initially involve several candidate models that describe the data-generating process. Analysis often proceeds by first selecting the best model according to some criterion and then learning about the parameters of this selected model. Crucially, however, in this approach the parameter estimates are conditioned on the selected model, and any uncertainty about the model-selection process is ignored. An alternative is to learn the parameters for all candidate models and then combine the estimates according to the posterior probabilities of the associated models. This approach is known as Bayesian model averaging (BMA). BMA has several important advantages over all-or-none selection methods, but has been used only sparingly in the social sciences. In this conceptual introduction, we explain the principles of BMA, describe its advantages over all-or-none model selection, and showcase its utility in three examples: analysis of covariance, meta-analysis, and network analysis.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\EMPTY_COLLECTION_NAME\Hinne_et_al-A_Conceptual_Introduction_to_Bayesian_Model_Averaging_2020.pdf}
}

@article{hoffman,
  title = {Stochastic {{Variational Inference}}},
	author = {Hoffman, Matthew D},
  abstract = {We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models, latent Dirichlet allocation and the hierarchical Dirichlet process topic model. Using stochastic variational inference, we analyze several large collections of documents: 300K articles from Nature, 1.8M articles from The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can easily handle data sets of this size and outperforms traditional variational inference, which can only handle a smaller subset. (We also show that the Bayesian nonparametric topic model outperforms its parametric counterpart.) Stochastic variational inference lets us apply complex Bayesian models to massive data sets.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\Y9ZQE9HP\Hoffman - Stochastic Variational Inference.pdf}
}

@article{hoffman2013,
  title = {Stochastic {{Variational Inference}}},
	author = {Hoffman, Matthew D},
  year = {2013},
  journal = {Journal of Machine Learning Research},
  volume = {14},
  pages = {45},
  abstract = {We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models, latent Dirichlet allocation and the hierarchical Dirichlet process topic model. Using stochastic variational inference, we analyze several large collections of documents: 300K articles from Nature, 1.8M articles from The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can easily handle data sets of this size and outperforms traditional variational inference, which can only handle a smaller subset. (We also show that the Bayesian nonparametric topic model outperforms its parametric counterpart.) Stochastic variational inference lets us apply complex Bayesian models to massive data sets.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Hoffman-Stochastic_Variational_Inference_2013.pdf}
}

@article{hoffman2014,
  title = {The {{No-U-Turn Sampler}}: {{Adaptively Setting Path Lengths}} in {{Hamiltonian Monte Carlo}}},
	author = {Hoffman, Matthew D and Gelman, Andrew},
  year = {2014},
  journal = {Journal of Machine Learning Research},
  volume = {15},
  pages = {31},
  abstract = {Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior and sensitivity to correlated parameters that plague many MCMC methods by taking a series of steps informed by first-order gradient information. These features allow it to converge to high-dimensional target distributions much more quickly than simpler methods such as random walk Metropolis or Gibbs sampling. However, HMC's performance is highly sensitive to two user-specified parameters: a step size and a desired number of steps L. In particular, if L is too small then the algorithm exhibits undesirable random walk behavior, while if L is too large the algorithm wastes computation. We introduce the No-U-Turn Sampler (NUTS), an extension to HMC that eliminates the need to set a number of steps L. NUTS uses a recursive algorithm to build a set of likely candidate points that spans a wide swath of the target distribution, stopping automatically when it starts to double back and retrace its steps. Empirically, NUTS performs at least as efficiently as (and sometimes more efficiently than) a well tuned standard HMC method, without requiring user intervention or costly tuning runs. We also derive a method for adapting the step size parameter on the fly based on primal-dual averaging. NUTS can thus be used with no hand-tuning at all, making it suitable for applications such as BUGS-style automatic inference engines that require efficient ``turnkey'' samplers.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Bayesian Inference\Hoﬀman_Gelman-The_No-U-Turn_Sampler_2014.pdf}
}

@article{hu2016,
  title = {A {{Single-Loop Kriging Surrogate Modeling}} for {{Time-Dependent Reliability Analysis}}},
	author = {Hu, Zhen and Mahadevan, Sankaran},
  year = {2016},
  journal = {Journal of Mechanical Design},
  volume = {138},
  number = {6},
  urldate = {2022-03-04},
  abstract = {Current surrogate modeling methods for time-dependent reliability analysis implement a double-loop procedure, with the computation of extreme value response in the outer loop and optimization in the inner loop. The computational effort of the double-loop procedure is quite high even though improvements have been made to improve the efficiency of the inner loop. This paper proposes a single-loop Kriging (SILK) surrogate modeling method for time-dependent reliability analysis. The optimization loop used in current methods is completely removed in the proposed method. A single surrogate model is built for the purpose of time-dependent reliability assessment. Training points of random variables and over time are generated at the same level instead of at two separate levels. The surrogate model is refined adaptively based on a learning function modified from time-independent reliability analysis and a newly developed convergence criterion. Strategies for building the surrogate model are investigated for problems with and without stochastic processes. Results of three numerical examples show that the proposed single-loop procedure significantly increases the efficiency of time-dependent reliability analysis without sacrificing the accuracy.},
  langid = {english}
}

@article{hu2018,
  title = {Model {{Discrepancy Quantification}} in {{Simulation-Based Design}} of {{Dynamical Systems}}},
	author = {Hu, Zhen and Hu, Chao and Mourelatos, Zissimos P. and Mahadevan, Sankaran},
  year = {2018},
  journal = {Journal of Mechanical Design},
  volume = {141},
  number = {011401},
  urldate = {2023-08-01},
  abstract = {Discrete-time state-space models have been extensively used in simulation-based design of dynamical systems. These prediction models may not accurately represent the true physics of a dynamical system due to potentially flawed understanding of the system, missing physics, and/or numerical approximations. To improve the validity of these models at new design locations, this paper proposes a novel dynamic model discrepancy quantification (DMDQ) framework. Time-instantaneous prediction models are constructed for the model discrepancies of ``hidden'' state variables, and are used to correct the discrete-time prediction models at each time-step. For discrete-time models, the hidden state variables and their discrepancies are coupled over two adjacent time steps. Also, the state variables cannot be directly measured. These factors complicate the construction of the model discrepancy prediction models. The proposed DMDQ framework overcomes these challenges by proposing two discrepancy modeling approaches: an estimation-modeling approach and a modeling-estimation approach. The former first estimates the model discrepancy and then builds a nonparametric prediction model of the model discrepancy; the latter builds a parametric prediction model of the model discrepancy first and then estimates the parameters of the prediction model. A subsampling method is developed to reduce the computational effort in building the two types of prediction models. A mathematical example and an electrical circuit dynamical system demonstrate the effectiveness of the proposed DMDQ framework and highlight the advantages and disadvantages of the proposed approaches.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Hu_et_al-Model_Discrepancy_Quantification_in_Simulation-Based_Design_of_Dynamical_Systems_2018.pdf}
}

@article{hu2021,
  title = {A Model Validation Framework Based on Parameter Calibration under Aleatory and Epistemic Uncertainty},
	author = {Hu, Jiexiang and Zhou, Qi and McKeand, Austin and Xie, Tingli and Choi, Seung-Kyum},
  year = {2021},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {63},
  number = {2},
  pages = {645--660},
  urldate = {2021-09-07},
  abstract = {Model validation methods have been widely used in engineering design to evaluate the accuracy and reliability of simulation models with uncertain inputs. Most of the existing validation methods for aleatory and epistemic uncertainty are based on the Bayesian theorem, which needs a vast number of data to update the posterior distribution of the model parameter. However, when a single simulation is time-consuming, the required simulation cost for the validation of a simulation model may be unaffordable. To overcome this difficulty, a new model validation framework based on parameter calibration under aleatory and epistemic uncertainty is proposed. In the proposed method, a stochastic kriging model is constructed to predict the validity of the candidate simulation model under different uncertainty input parameters. Then, an optimization problem is defined to calibrate the epistemic uncertainty parameters to minimize the discrepancy between the simulation model and the experimental model. K--S test finally decides whether to accept or reject the calibrated simulation model. The performance of the proposed approach is illustrated through a cantilever beam example and a turbine blade validation problem. Results show that the proposed framework can identify the most appropriate parameters to calibrate the simulation model and provide a correct judgment about the validity of the candidate model, which is useful for the validation of simulation models in practical engineering design.},
  langid = {english},
  keywords = {Area Metric,Framework,Gaussian processes,Kriging,Model Calibration,Model Validation,Uncertainty},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Frameworks\Hu_et_al-A_model_validation_framework_based_on_parameter_calibration_under_aleatory_and_2021.pdf}
}

@article{huang2020,
  title = {Thermomechanical Properties and Fatigue Life Evaluation of {{SnAgCu}} Solder Joints for Microelectronic Power Module Application},
	author = {Huang, Xiaoguang and Wang, Zhiqiang and Yu, Yanqun},
  year = {2020},
  journal = {Journal of Materials Research and Technology},
  volume = {9},
  number = {3},
  pages = {5533--5541},
  urldate = {2023-05-30},
  abstract = {In this paper, a new constitutive model of SnAgCu lead-free solder, which covered the low-temperature and elevated-temperature creep properties, was constructed according to the thermomechanical property test under a wide range of temperatures (-40 to 120{$^\circ$}C). This model was then implemented to the finite element model for simulation of the cyclic creep deformation of Sn3Ag0.5Cu solder in a chip inside the microelectronic power module (MPM). The accumulated creep strain of the solder layer was calculated and used to predict the thermo-mechanical fatigue life of the MPM. The applicability of the life prediction method was evaluated through a cross-check of the present results with that obtained by a double power model in the literature, as well as the thermo-mechanical fatigue test results. It was found that the thermo-mechanical fatigue lives, estimated by the accumulated creep strain and creep strain energy density from the established hyperbolic sine power law, are closer to the test results than that estimated by the double power law. The presented model can be seen as an improvement on the existing constitutive models of SnAgCu lead-free solder.},
  langid = {english},
  keywords = {Constitutive model,Creep strain,Life prediction,Sn3Ag0.5Cu solder,Strain energy density},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Lifetime Coffin Manson\\Huang_et_al-Thermomechanical_properties_and_fatigue_life_evaluation_of_SnAgCu_solder_joints_2020.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\LEMTWRLQ\\S2238785419307380.html}
}

@misc{huang2022,
  title = {Quantifying {{Epistemic Uncertainty}} in {{Deep Learning}}},
	author = {Huang, Ziyi and Lam, Henry and Zhang, Haofeng},
  year = {2022},
  number = {arXiv:2110.12122},
  eprint = {2110.12122},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-01-13},
  abstract = {Uncertainty quantification is at the core of the reliability and robustness of machine learning. In this paper, we provide a theoretical framework to dissect the uncertainty, especially the epistemic component, in deep learning into procedural variability (from the training procedure) and data variability (from the training data), which is the first such attempt in the literature to our best knowledge. We then propose two approaches to estimate these uncertainties, one based on influence function and one on batching. We demonstrate how our approaches overcome the computational difficulties in applying classical statistical methods. Experimental evaluations on multiple problem settings corroborate our theory and illustrate how our framework and estimation can provide direct guidance on modeling and data collection effort to improve deep learning performance.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning,Statistics - Methodology},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Uncertainty Quantification\\Huang_et_al-Quantifying_Epistemic_Uncertainty_in_Deep_Learning_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\AZLTK2QH\\2110.html}
}

@article{hullermeier2021,
  title = {Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods},
  shorttitle = {Aleatoric and Epistemic Uncertainty in Machine Learning},
	author = {H{\"u}llermeier, Eyke and Waegeman, Willem},
  year = {2021},
  journal = {Machine Learning},
  volume = {110},
  number = {3},
  pages = {457--506},
  urldate = {2023-01-13},
  abstract = {Abstract                            The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often referred to as               aleatoric               and               epistemic               . In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of attempts so far at handling uncertainty in general and formalizing this distinction in particular.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Uncertainty Quantification\Hullermeier_Waegeman-Aleatoric_and_epistemic_uncertainty_in_machine_learning_2021.pdf}
}

@article{huntington1998,
  title = {Improvements to and Limitations of {{Latin}} Hypercube Sampling},
	author = {Huntington, D.E. and Lyrintzis, C.S.},
  year = {1998},
  journal = {Probabilistic Engineering Mechanics},
  volume = {13},
  number = {4},
  pages = {245--253},
  urldate = {2022-09-27},
  langid = {english}
}

@book{IEC61508,
  title = {{{IEC}} 61508:2010 {{Functional}} Safety of Electrical/Electronic/Programmable Electronic Safety-Related Systems},
  year = {2010},
  publisher = {International Electrotechnical Commission},
  address = {Geneva, Switzerland}
}

@inproceedings{ishigami1991,
  title = {An Importance Quantification Technique in Uncertainty Analysis for Computer Models},
  booktitle = {First {{International Symposium}} on {{Uncertainty Modeling}} and {{Analysis}}},
	author = {Ishigami, T. and Homma, T.},
  year = {1991},
  pages = {398--403},
  publisher = {IEEE Comput. Soc. Press},
  address = {College Park, MD, USA},
  urldate = {2022-01-20},
}

@book{ISO26262,
  title = {{{ISO26262}}:2018 {{Road}} Vehicles --- Functional Safety},
  year = {2018},
  publisher = {International Organization for Standardization},
  address = {Geneva, Switzerland}
}

@misc{ivanova2021,
  title = {Implicit {{Deep Adaptive Design}}: {{Policy-Based Experimental Design}} without {{Likelihoods}}},
  shorttitle = {Implicit {{Deep Adaptive Design}}},
	author = {Ivanova, Desi R. and Foster, Adam and Kleinegesse, Steven and Gutmann, Michael U. and Rainforth, Tom},
  year = {2021},
  number = {arXiv:2111.02329},
  eprint = {2111.02329},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {We introduce implicit Deep Adaptive Design (iDAD), a new method for performing adaptive experiments in real-time with implicit models. iDAD amortizes the cost of Bayesian optimal experimental design (BOED) by learning a design policy network upfront, which can then be deployed quickly at the time of the experiment. The iDAD network can be trained on any model which simulates differentiable samples, unlike previous design policy work that requires a closed form likelihood and conditionally independent experiments. At deployment, iDAD allows design decisions to be made in milliseconds, in contrast to traditional BOED approaches that require heavy computation during the experiment itself. We illustrate the applicability of iDAD on a number of experiments, and show that it provides a fast and effective mechanism for performing adaptive design with implicit models.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning,Statistics - Computation,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Design of Experiments\\Adaptive Methods\\Ivanova_et_al-Implicit_Deep_Adaptive_Design_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\FA7EFIA4\\2111.html}
}

@misc{jankowiak2020,
  title = {Parametric {{Gaussian Process Regressors}}},
	author = {Jankowiak, Martin and Pleiss, Geoff and Gardner, Jacob R.},
  year = {2020},
  number = {arXiv:1910.07123},
  eprint = {1910.07123},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-06-28},
  abstract = {The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially underestimated uncertainties. Notably, in the regression case the predictive variance is typically dominated by observation noise, yielding uncertainty estimates that make little use of the input-dependent function uncertainty that makes GP priors attractive. In this work we propose two simple methods for scalable GP regression that address this issue and thus yield substantially improved predictive uncertainties. The first applies variational inference to FITC (Fully Independent Training Conditional; Snelson et.{\textasciitilde}al.{\textasciitilde}2006). The second bypasses posterior approximations and instead directly targets the posterior predictive distribution. In an extensive empirical comparison with a number of alternative methods for scalable GP regression, we find that the resulting predictive distributions exhibit significantly better calibrated uncertainties and higher log likelihoods--often by as much as half a nat per datapoint.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Jankowiak_et_al-Parametric_Gaussian_Process_Regressors_2020.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\NEKP7SFE\\1910.html}
}

@book{jeffreys1939,
  title = {Theory of {{Probability}}},
	author = {Jeffreys, Harold},
  year = {1939},
  edition = {1st},
  publisher = {Oxford University Press},
  address = {Oxford, England},
  langid = {english}
}

@article{jiang2020,
  title = {A Sequential Calibration and Validation Framework for Model Uncertainty Quantification and Reduction},
	author = {Jiang, Chen and Hu, Zhen and Liu, Yixuan and Mourelatos, Zissimos P. and Gorsich, David and others},
  year = {2020},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {368},
  urldate = {2021-09-07},
  abstract = {This paper aims to provide new insights into model calibration, which plays an essential role in improving the validity of Modeling and Simulation (M\&S) in engineering design and analysis. Various existing model calibration approaches including the direct Bayesian calibration method, the well-known Kennedy and O'Hagan (KOH) framework and its variants, and the optimization-based calibration method, are first investigated. It is observed that the direct Bayesian calibration and optimizationbased calibration may be misled by potentially wrong information if the computer model cannot adequately capture the underlying true physics, while the effectiveness of the KOH framework and its variants is significantly affected by the prior distributions of the unknown model parameters. Based on this observation, a sequential model calibration and validation (SeCAV) framework is proposed to improve the efficacy of both model parameter calibration and bias correction for the purpose of uncertainty quantification and reduction. In the proposed method, the model validation and Bayesian calibration are implemented in a sequential manner, where the former serves as a filter to select the best experimental data for the latter, and provides the latter with a confidence probability as a weight factor for updating the uncertain model parameters. The parameter calibration result is then integrated with model bias correction to improve the prediction accuracy of the M\&S. A mathematical example and an engineering example are employed to demonstrate the advantages and disadvantages of different approaches. The results show that the SeCAV framework, in general, performs better than the existing methods.},
  langid = {english},
  keywords = {Bayesian,Framework,Gaussian processes,Metamodeling,Model Calibration,Surrogate Model,Uncertainty Quantification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Jiang_et_al-A_sequential_calibration_and_validation_framework_for_model_uncertainty_2020.pdf}
}

@inproceedings{jin2002,
  title = {On {{Sequential Sampling}} for {{Global Metamodeling}} in {{Engineering Design}}},
  booktitle = {Volume 2: 28th {{Design Automation Conference}}},
	author = {Jin, Ruichen and Chen, Wei and Sudjianto, Agus},
  year = {2002},
  pages = {539--548},
  publisher = {ASMEDC},
  address = {Montreal, Quebec, Canada},
  urldate = {2022-08-05},
  abstract = {Approximation models (also known as metamodels) have been widely used in engineering design to facilitate analysis and optimization of complex systems that involve computationally expensive simulation programs. The accuracy of metamodels is directly related to the sampling strategies used. Our goal in this paper is to investigate the general applicability of sequential sampling for creating global metamodels. Various sequential sampling approaches are reviewed and new approaches are proposed. The performances of these approaches are investigated against that of the onestage approach using a set of test problems with a variety of features. The potential usages of sequential sampling strategies are also discussed.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Jin_et_al-On_Sequential_Sampling_for_Global_Metamodeling_in_Engineering_Design_2002.pdf}
}

@article{jo2021,
  title = {Optimization-Based Model Calibration of Marginal and Joint Output Distributions Utilizing Analytical Gradients},
	author = {Jo, Hwisang and Lee, Kyungeun and Lee, Mingyu and Jung, Yongsu and Lee, Ikjin},
  year = {2021},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {63},
  number = {6},
  pages = {2853--2868},
  urldate = {2023-05-10},
  abstract = {Optimization-based model calibration (OBMC) determines statistical parameters of unknown input variables by optimizing statistical similarity between simulations and observations. Gradient-based optimization algorithms have been utilized for OBMC since they require less computational cost compared with non-gradient optimization algorithms. However, OBMC using numerical gradients such as finite differences has disadvantages in the aspect of computational cost and numerical instability. For these reasons, a previous study derived analytical gradients under the assumption that performance functions are a linear single response and unknown inputs follow a normal distribution. However, to apply the model calibration to general engineering problems, analytical gradients need to be derived without any assumption. Therefore, it is proposed in this study to derive analytical gradients of marginal and joint likelihood functions to calibrate both linear and nonlinear responses. In addition, the analytical gradients are derived for five distribution types of unknown input random variables to be estimated: normal, lognormal, Gumbel, extreme, and uniform distributions. For derivation of the analytical gradients, the chain rule is utilized to combine the derivatives of the inverse function of cumulative distribution function (CDF), performance function, and joint likelihood function. Numerical examples and one engineering example using finite element analysis (FEA) are employed to verify the accuracy and efficiency of the proposed analytical gradient, and it is demonstrated that accurately calibrated output responses can be obtained by the proposed method by finding a better optimum in OBMC.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\NBP5KDZ2\Jo et al. - 2021 - Optimization-based model calibration of marginal a.pdf}
}

@article{joe2008,
  title = {Constructing {{Sobol Sequences}} with {{Better Two-Dimensional Projections}}},
	author = {Joe, Stephen and Kuo, Frances Y.},
  year = {2008},
  journal = {SIAM Journal on Scientific Computing},
  volume = {30},
  number = {5},
  pages = {2635--2654},
  urldate = {2024-02-01},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Joe_Kuo-Constructing_Sobol_Sequences_with_Better_Two-Dimensional_Projections_2008.pdf}
}

@article{jones1998,
  title = {Efficient {{Global Optimization}} of {{Expensive Black-Box Functions}}.},
	author = {Jones, Donald R. and Schonlau, Matthias and Welch, William J.},
  year = {1998},
  journal = {Journal of Global Optimization},
  volume = {13},
  number = {4},
  pages = {455--492},
  urldate = {2022-02-14}
}

@article{jospin2022,
  title = {Hands-on {{Bayesian Neural Networks}} -- a {{Tutorial}} for {{Deep Learning Users}}},
	author = {Jospin, Laurent Valentin and Buntine, Wray and Boussaid, Farid and Laga, Hamid and Bennamoun, Mohammed},
  year = {2022},
  journal = {arXiv:2007.06823},
  eprint = {2007.06823},
  urldate = {2022-01-21},
  abstract = {Modern deep learning methods constitute incredibly powerful tools to tackle a myriad of challenging problems. However, since deep learning methods operate as black boxes, the uncertainty associated with their predictions is often challenging to quantify. Bayesian statistics offer a formalism to understand and quantify the uncertainty associated with deep neural network predictions. This tutorial provides deep learning practitioners with an overview of the relevant literature and a complete toolset to design, implement, train, use and evaluate Bayesian neural networks, i.e., stochastic artificial neural networks trained using Bayesian methods.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {62-02 (Primary),Computer Science - Machine Learning,G.3,I.2.6,Statistics - Machine Learning},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Bayesian Neural Networks\Jospin_et_al-Hands-on_Bayesian_Neural_Networks_--_a_Tutorial_for_Deep_Learning_Users_2022.pdf}
}

@article{jung2015,
  title = {A Framework of Model Validation and Virtual Product Qualification with Limited Experimental Data Based on Statistical Inference},
	author = {Jung, Byung C. and Park, Jungho and Oh, Hyunseok and Kim, Jisun and Youn, Byeng D.},
  year = {2015},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {51},
  number = {3},
  pages = {573--583},
  urldate = {2021-09-07},
  abstract = {Virtual testing is a recent engineering development trend to design, evaluate, and test new engineered products. This research proposes a framework of virtual testing based on statistical inference for new product development comprising of three successive steps: (i) statistical model calibration, (ii) hypothesis test for validity check and (iii) virtual qualification. Statistical model calibration first improves the predictive capability of a computational model in a calibration domain. Next, the hypothesis test is performed with limited observed data to see if a calibrated model is sufficiently predictive for virtual testing of a new product design. An area metric and the u-pooling method are employed for the hypothesis test to measure the degree of mismatch between predicted and observed results while considering statistical uncertainty in the area metric due to the lack of experimental data. Once the calibrated model becomes valid, the virtual qualification process can be executed with a qualified model for new product developments. The qualification process builds a design decision matrix to aid in rational decision-making for product design alternatives. The effectiveness of the proposed framework is demonstrated through the case study of a tire tread block.},
  langid = {english},
  keywords = {Area Metric,Framework,Hypothesis Testing,Model Validation,U-Pooling},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\Promotion Model Validation\Model Validation\Frameworks\Jung_et_al-A_framework_of_model_validation_and_virtual_product_qualification_with_limited_2015.pdf}
}

@article{jung2020,
  title = {A {{Response-Adaptive Method}} for {{Design}} of {{Validation Experiments}} in {{Computational Mechanics}}},
	author = {Jung, Byung C. and Shin, Yun-Ho and Lee, Sang Hyuk and Huh, Young Cheol and Oh, Hyunseok},
  year = {2020},
  journal = {Applied Sciences},
  volume = {10},
  number = {2},
  pages = {647},
  urldate = {2021-09-07},
  abstract = {For model verification and validation (V \& V) in computational mechanics, a hypothesis test for the validity check (HTVC) is useful, in particular, with a limited number of experimental data. However, HTVC does not address how type I and II errors can be reduced when additional resources for sampling become available. For the validation of computational models of safety-related and mission-critical systems, it is challenging to design experiments so that type II error is reduced while maintaining type I error at an acceptable level. To address the challenge, this paper proposes a new method to design validation experiments, response-adaptive experiment design (RAED). The RAED method adaptively selects the next experimental condition from among candidates of various operating conditions (experimental settings). RAED consists of six key steps: (1) define experimental conditions, (2) obtain experimental data, (3) calculate u-values, (4) compute the area metric, (5) select the next experimental condition, and (6) obtain additional experimental datum. To demonstrate the effectiveness of the RAED method, a case study of a numerical example is shown. It is demonstrated that additional experimental data obtained through the RAED method can reduce type II error in hypothesis testing and increase the probability of rejecting an invalid computational model.},
  langid = {english},
  keywords = {Adaptive Sampling,Area Metric,Efficient Model Validation,Model Validation,To Implement,U-Pooling,Validation Metric},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\Promotion Model Validation\Model Validation\Efficient Model Validation\Jung_et_al-A_Response-Adaptive_Method_for_Design_of_Validation_Experiments_in_2020.pdf}
}

@article{jung2022,
  title = {Statistical Model Calibration and Design Optimization under Aleatory and Epistemic Uncertainty},
	author = {Jung, Yongsu and Jo, Hwisang and Choo, Jeonghwan and Lee, Ikjin},
  year = {2022},
  journal = {Reliability Engineering \& System Safety},
  volume = {222},
  pages = {108428},
  urldate = {2023-05-10},
  abstract = {Statistical model calibration is a framework for inference on unknown model parameters and modeling discrepancy between simulation and experiment through an inverse method in the presence of uncertainty. Most of the existing approaches cannot treat aleatory uncertainty of model parameters and model discrepancy simultaneously, and thus reliability analysis and design optimization using a calibrated simulation model ac\- counting for uncertainty have been limitedly applied. Therefore, a statistical model calibration using stochastic Kriging accounting for the aleatory uncertainty of model parameters is proposed in this paper. The probability distributions of the model parameters and corresponding discrepancy are quantified and estimated through the maximum likelihood estimation (MLE). Since it may be difficult to secure sufficient experimental data for model calibration due to limited resources, the quantification of epistemic uncertainty on the calibrated model and propagation to reliability are also presented. Then, the design optimization accounting for aleatory and epistemic uncertainty, which is called confidence-based design optimization (CBDO), can yield the conservative optimum to prevent the unexpected failure. In conclusion, the proposed framework facilitates the statistical model cali\- bration and design optimization under aleatory uncertainty of model parameters and model discrepancy and epistemic uncertainty caused by insufficient data.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\YARP7MUM\Jung et al. - 2022 - Statistical model calibration and design optimizat.pdf}
}

@book{kaipio2005,
  title = {Statistical and {{Computational Inverse Problems}}},
	author = {Kaipio, Jari P. and Somersalo, Erkki},
  year = {2005},
  series = {Applied {{Mathematical Sciences}}},
  volume = {160},
  publisher = {Springer New York},
  address = {New York, NY},
  urldate = {2023-07-28},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Kaipio_Somersalo-Statistical_and_Computational_Inverse_Problems_22.pdf}
}

@article{kapusuzoglu2023,
  title = {Multi-{{Level Bayesian Calibration}} of a {{Multi-Component Dynamic System Model}}},
	author = {Kapusuzoglu, Berkcan and Mahadevan, Sankaran and Matsumoto, Shunsaku and Miyagi, Yoshitomo and Watanabe, Daigo},
  year = {2023},
  journal = {Journal of Computing and Information Science in Engineering},
  volume = {23},
  number = {1},
  pages = {011006},
  urldate = {2023-05-10},
  abstract = {Abstract             This paper proposes a multi-level Bayesian calibration approach that fuses information from heterogeneous sources and accounts for uncertainties in modeling and measurements for time-dependent multi-component systems. The developed methodology has two elements: quantifying the uncertainty at component and system levels, by fusing all available information, and corrected model prediction. A multi-level Bayesian calibration approach is developed to estimate component-level and system-level parameters using measurement data that are obtained at different time instances for different system components. Such heterogeneous data are consumed in a sequential manner, and an iterative strategy is developed to calibrate the parameters at the two levels. This calibration strategy is implemented for two scenarios: offline and online. The offline calibration uses data that is collected over all the time-steps, whereas online calibration is performed in real-time as new measurements are obtained at each time-step. Analysis models and observation data for the thermo-mechanical behavior of gas turbine engine rotor blades are used to analyze the effectiveness of the proposed approach.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\73TXXFEP\Kapusuzoglu et al. - 2023 - Multi-Level Bayesian Calibration of a Multi-Compon.pdf}
}

@article{karniadakis2021,
  title = {Physics-Informed Machine Learning},
	author = {Karniadakis, George Em and Kevrekidis, Ioannis G. and Lu, Lu and Perdikaris, Paris and Wang, Sifan and others},
  year = {2021},
  journal = {Nature Reviews Physics},
  volume = {3},
  number = {6},
  pages = {422--440},
  publisher = {Nature Publishing Group},
  urldate = {2023-06-13},
  abstract = {Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Here, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems.},
  copyright = {2021 Springer Nature Limited},
  langid = {english},
  keywords = {Applied mathematics,Computational science},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Karniadakis_et_al-Physics-informed_machine_learning_2021.pdf}
}

@article{kaymaz2005,
  title = {Application of Kriging Method to Structural Reliability Problems},
	author = {Kaymaz, Irfan},
  year = {2005},
  journal = {Structural Safety},
  volume = {27},
  number = {2},
  pages = {133--151},
  urldate = {2024-01-12},
  abstract = {Approximation methods are widely used to alleviate the computational burden of engineering analyses. For structural reliability analyses, the common approach is to use the response surface method (RSM) based on the least square regression. However, another approximation method based on kriging has gained popularity especially in the field of deterministic optimization. However, the application of the kriging method to structural reliability problems has not been realized until recently. Therefore, this paper investigates the use of the kriging method for structural reliability problems by comparing it with the most common RSM. The effects of the kriging parameters are also examined on the basis of the {$\beta$} computation and fitting behavior. It can be deduced from the results given in this paper that using the most common approach in the literature to find the kriging parameters does not guarantee a good result for the structural reliability problems. As a result, some advantages as well as disadvantages of the kriging method are reported, based on the results obtained from the application of the kriging method to the examples from the literature. Finally, this paper suggests the points for which the kriging model could be improved to get better results for structural reliability problems.},
  keywords = {Kriging approximation,Response surface methods,Structural reliability},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\EX6WYBNR\S0167473004000463.html}
}

@article{kennedy2001,
  title = {Bayesian Calibration of Computer Models},
	author = {Kennedy, Marc C. and O'Hagan, Anthony},
  year = {2001},
  journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume = {63},
  number = {3},
  pages = {425--464},
  urldate = {2021-09-07},
  abstract = {We consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models. Such models, implemented as computer codes, are often generic in the sense that by a suitable choice of some of the model's input parameters the code can be used to predict the behaviour of the system in a variety of speci{\textregistered}c applications. However, in any speci{\textregistered}c application the values of necessary parameters may be unknown. In this case, physical observations of the system in the speci{\textregistered}c context are used to learn about the unknown parameters. The process of {\textregistered}tting the model to the observed data by adjusting the parameters is known as calibration. Calibration is typically effected by ad hoc {\textregistered}tting, and after calibration the model is used, with the {\textregistered}tted input values, to predict the future behaviour of the system. We present a Bayesian calibration technique which improves on this traditional approach in two respects. First, the predictions allow for all sources of uncertainty, including the remaining uncertainty over the {\textregistered}tted parameters. Second, they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best-{\textregistered}tting parameter values. The method is illustrated by using data from a nuclear radiation release at Tomsk, and from a more complex simulated nuclear accident exercise.},
  langid = {english},
  keywords = {Bayesian,Comparison,Framework,Gaussian processes,Kennedy O'Hagan Framework,Model Calibration,To Implement},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\Promotion Model Validation\Model Calibration\Kennedy_O'Hagan-Bayesian_calibration_of_computer_models_2001.pdf}
}

@article{kennedy2001a,
  title = {Bayesian {{Calibration}} of {{Computer Models}}},
	author = {Kennedy, Marc C. and O'Hagan, Anthony},
  year = {2001},
  journal = {Journal of the Royal Statistical Society Series B: Statistical Methodology},
  volume = {63},
  number = {3},
  pages = {425--464},
  urldate = {2023-05-10},
  abstract = {We consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models. Such models, implemented as computer codes, are often generic in the sense that by a suitable choice of some of the model's input parameters the code can be used to predict the behaviour of the system in a variety of speci{\textregistered}c applications. However, in any speci{\textregistered}c application the values of necessary parameters may be unknown. In this case, physical observations of the system in the speci{\textregistered}c context are used to learn about the unknown parameters. The process of {\textregistered}tting the model to the observed data by adjusting the parameters is known as calibration. Calibration is typically effected by ad hoc {\textregistered}tting, and after calibration the model is used, with the {\textregistered}tted input values, to predict the future behaviour of the system. We present a Bayesian calibration technique which improves on this traditional approach in two respects. First, the predictions allow for all sources of uncertainty, including the remaining uncertainty over the {\textregistered}tted parameters. Second, they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best-{\textregistered}tting parameter values. The method is illustrated by using data from a nuclear radiation release at Tomsk, and from a more complex simulated nuclear accident exercise.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\3RQK58Q5\Kennedy and O'Hagan - 2001 - Bayesian Calibration of Computer Models.pdf}
}

@article{kennedy2001b,
  title = {Bayesian {{Calibration}} of {{Computer Models}}},
	author = {Kennedy, Marc C. and O'Hagan, Anthony},
  year = {2001},
  journal = {Journal of the Royal Statistical Society Series B: Statistical Methodology},
  volume = {63},
  number = {3},
  pages = {425--464},
  urldate = {2023-05-10},
  abstract = {We consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models. Such models, implemented as computer codes, are often generic in the sense that by a suitable choice of some of the model's input parameters the code can be used to predict the behaviour of the system in a variety of speci{\textregistered}c applications. However, in any speci{\textregistered}c application the values of necessary parameters may be unknown. In this case, physical observations of the system in the speci{\textregistered}c context are used to learn about the unknown parameters. The process of {\textregistered}tting the model to the observed data by adjusting the parameters is known as calibration. Calibration is typically effected by ad hoc {\textregistered}tting, and after calibration the model is used, with the {\textregistered}tted input values, to predict the future behaviour of the system. We present a Bayesian calibration technique which improves on this traditional approach in two respects. First, the predictions allow for all sources of uncertainty, including the remaining uncertainty over the {\textregistered}tted parameters. Second, they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best-{\textregistered}tting parameter values. The method is illustrated by using data from a nuclear radiation release at Tomsk, and from a more complex simulated nuclear accident exercise.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\QNIZ9TCQ\Kennedy and O'Hagan - 2001 - Bayesian Calibration of Computer Models.pdf}
}

@article{kennedy2001c,
  title = {Supplementary Details on Bayesian Calibration of Computer Models},
	author = {Kennedy, Marc C. and O'Hagan, Anthony},
  year = {2001},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\DBC\KOH\Kennedy_O'Hagan-Supplementary_details_on_bayesian_calibration_of_computer_models_2001.pdf}
}

@inproceedings{kersting2007,
  title = {Most Likely Heteroscedastic {{Gaussian}} Process Regression},
  booktitle = {Proceedings of the 24th International Conference on {{Machine}} Learning},
	author = {Kersting, Kristian and Plagemann, Christian and Pfaff, Patrick and Burgard, Wolfram},
  year = {2007},
  pages = {393--400},
  publisher = {ACM},
  address = {Corvalis Oregon USA},
  urldate = {2023-01-13},
  langid = {english}
}

@article{khan,
  title = {The {{Bayesian Learning Rule}}},
	author = {Khan, Mohammad Emtiyaz},
  abstract = {We show that many machine-learning algorithms are specific instances of a single algorithm called the Bayesian learning rule. The rule, derived from Bayesian principles, yields a wide-range of algorithms from fields such as optimization, deep learning, and graphical models. This includes classical algorithms such as ridge regression, Newton's method, and Kalman filter, as well as modern deep-learning algorithms such as stochastic-gradient descent, RMSprop, and Dropout. The key idea in deriving such algorithms is to approximate the posterior using candidate distributions estimated by using natural gradients. Different candidate distributions result in different algorithms and further approximations to natural gradients give rise to variants of those algorithms. Our work not only unifies, generalizes, and improves existing algorithms, but also helps us design new ones.},
  langid = {english}
}

@article{khan2023,
  title = {The Bayesian Learning Rule},
	author = {Khan, Mohammad Emtiyaz and Rue, H{\aa}vard},
  year = {2023},
  journal = {Journal of Machine Learning Research},
  volume = {24},
  number = {281},
  pages = {1--46},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\NL9C34G7\Khan - The Bayesian Learning Rule.pdf}
}

@misc{kim2019,
  title = {Attentive {{Neural Processes}}},
	author = {Kim, Hyunjik and Mnih, Andriy and Schwarz, Jonathan and Garnelo, Marta and Eslami, Ali and others},
  year = {2019},
  number = {arXiv:1901.05761},
  eprint = {1901.05761},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {Neural Processes (NPs) (Garnelo et al 2018a;b) approach regression by learning to map a context set of observed input-output pairs to a distribution over regression functions. Each function models the distribution of the output given an input, conditioned on the context. NPs have the benefit of fitting observed data efficiently with linear complexity in the number of context input-output pairs, and can learn a wide family of conditional distributions; they learn predictive distributions conditioned on context sets of arbitrary size. Nonetheless, we show that NPs suffer a fundamental drawback of underfitting, giving inaccurate predictions at the inputs of the observed data they condition on. We address this issue by incorporating attention into NPs, allowing each input location to attend to the relevant context points for the prediction. We show that this greatly improves the accuracy of predictions, results in noticeably faster training, and expands the range of functions that can be modelled.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Neural Process\\Kim_et_al-Attentive_Neural_Processes_2019.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\LH2PXDE6\\1901.html}
}

@inproceedings{kingma2015,
  title = {Adam: {{A Method}} for {{Stochastic Optimization}}.},
  shorttitle = {Adam},
  booktitle = {International {{Conference}} for {{Learning Representations}}},
	author = {Kingma, Diederik P. and Ba, Jimmy},
  year = {2015},
  urldate = {2022-01-21},
  abstract = {We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.},
  langid = {english},
  keywords = {Computer Science - Machine Learning},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\URMIZUUH\1412.html}
}

@article{kiureghian2009,
  title = {Aleatory or Epistemic? {{Does}} It Matter?},
  shorttitle = {Aleatory or Epistemic?},
	author = {Kiureghian, Armen Der and Ditlevsen, Ove},
  year = {2009},
  journal = {Structural Safety},
  series = {Risk {{Acceptance}} and {{Risk Communication}}},
  volume = {31},
  number = {2},
  pages = {105--112},
  urldate = {2023-06-30},
  abstract = {The sources and characters of uncertainties in engineering modeling for risk and reliability analyses are discussed. While many sources of uncertainty may exist, they are generally categorized as either aleatory or epistemic. Uncertainties are characterized as epistemic, if the modeler sees a possibility to reduce them by gathering more data or by refining models. Uncertainties are categorized as aleatory if the modeler does not foresee the possibility of reducing them. From a pragmatic standpoint, it is useful to thus categorize the uncertainties within a model, since it then becomes clear as to which uncertainties have the potential of being reduced. More importantly, epistemic uncertainties may introduce dependence among random events, which may not be properly noted if the character of uncertainties is not correctly modeled. Influences of the two types of uncertainties in reliability assessment, codified design, performance-based engineering and risk-based decision-making are discussed. Two simple examples demonstrate the influence of statistical dependence arising from epistemic uncertainties on systems and time-variant reliability problems.},
  langid = {english},
  keywords = {Aleatory,Epistemic,Ergodicity,Parameter uncertainty,Predictive models,Probability distribution choice,Statistical dependence,Systems,Time-variant reliability,Uncertainty},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Uncertainty Quantification\\Kiureghian_Ditlevsen-Aleatory_or_epistemic_2009.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\BVDEZVW5\\S0167473008000556.html}
}

@article{klemenc2013,
  title = {Joint Estimation of {{E}}--{{N}} Curves and Their Scatter Using Evolutionary Algorithms},
	author = {Klemenc, Jernej and Fajdiga, Matija},
  year = {2013},
  journal = {International Journal of Fatigue},
  volume = {56},
  pages = {42--53},
  urldate = {2023-05-30},
  abstract = {We present an approach for estimating E--N curves and their scatter. The scatter of a number of load cycles to failure at an arbitrary amplitude-strain level is modelled using a two-parametric Weibull distribution with the constant shape parameter {$\beta$} and the scale parameter {$\eta$} dependent on the strain amplitude by the Coffin--Manson equation. In this way the E--N curve and its scatter can be described using five parameters: the four parameters of the Coffin--Manson equation for the scale parameter of the Weibull distribution and the shape parameter of the Weibull distribution. The objective was to estimate these five parameters, which are generally unknown (since the data from the literature are manly known only for the median E--N curves), on the basis of the known fatigue-life data to obtain not only the trend of the E--N curve, but also its scatter. In order to estimate these parameters on the basis of the fatigue-life data, two evolutionary algorithms were applied: a real-valued genetic algorithm (GA) and the differential ant-stigmergy algorithm (DASA). In the article a mathematical background of the approach is presented and applied to 27 test cases of simulated fatigue-life data and one real case of experimentally obtained fatigue-life data. The results are analysed and discussed.},
  langid = {english},
  keywords = {AlSi9Cu3 alloy,Differential ant-stigmergy algorithm,E-N curves,Real-valued genetic algorithm,Weibull distribution},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\Lifetime Coffin Manson\\Klemenc_Fajdiga-Joint_estimation_of_E–N_curves_and_their_scatter_using_evolutionary_algorithms_2013.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\L6MN53UR\\S014211231300220X.html}
}

@misc{knoblauch2019,
  title = {Generalized {{Variational Inference}}: {{Three}} Arguments for Deriving New {{Posteriors}}},
  shorttitle = {Generalized {{Variational Inference}}},
	author = {Knoblauch, Jeremias and Jewson, Jack and Damoulas, Theodoros},
  year = {2019},
  number = {arXiv:1904.02063},
  eprint = {1904.02063},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-02-06},
  abstract = {We advocate an optimization-centric view on and introduce a novel generalization of Bayesian inference. Our inspiration is the representation of Bayes' rule as infinite-dimensional optimization problem (Csiszar, 1975; Donsker and Varadhan; 1975, Zellner; 1988). First, we use it to prove an optimality result of standard Variational Inference (VI): Under the proposed view, the standard Evidence Lower Bound (ELBO) maximizing VI posterior is preferable to alternative approximations of the Bayesian posterior. Next, we argue for generalizing standard Bayesian inference. The need for this arises in situations of severe misalignment between reality and three assumptions underlying standard Bayesian inference: (1) Well-specified priors, (2) well-specified likelihoods, (3) the availability of infinite computing power. Our generalization addresses these shortcomings with three arguments and is called the Rule of Three (RoT). We derive it axiomatically and recover existing posteriors as special cases, including the Bayesian posterior and its approximation by standard VI. In contrast, approximations based on alternative ELBO-like objectives violate the axioms. Finally, we study a special case of the RoT that we call Generalized Variational Inference (GVI). GVI posteriors are a large and tractable family of belief distributions specified by three arguments: A loss, a divergence and a variational family. GVI posteriors have appealing properties, including consistency and an interpretation as approximate ELBO. The last part of the paper explores some attractive applications of GVI in popular machine learning models, including robustness and more appropriate marginals. After deriving black box inference schemes for GVI posteriors, their predictive performance is investigated on Bayesian Neural Networks and Deep Gaussian Processes, where GVI can comprehensively improve upon existing methods.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Statistics\\Bayesian Inference\\Knoblauch_et_al-Generalized_Variational_Inference_2019.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\4B28JB8Y\\1904.html}
}

@misc{koermer2023,
  title = {Active {{Learning}} for {{Simulator Calibration}}},
	author = {Koermer, Scott and Loda, Justin and Noble, Aaron and Gramacy, Robert B.},
  year = {2023},
  number = {arXiv:2301.10228},
  eprint = {2301.10228},
  primaryclass = {stat},
  publisher = {arXiv},
  urldate = {2023-09-18},
  abstract = {The Kennedy and O'Hagan (KOH) calibration framework uses coupled Gaussian processes (GPs) to meta-model an expensive simulator (first GP), tune its 'knobs' (calibration inputs) to best match observations from a real physical/field experiment and correct for any modeling bias (second GP) when predicting under novel field conditions (design inputs). There are well-established methods for placement of design inputs for data-efficient planning of a simulation campaign in isolation, i.e., without field data: space-filling, or via criteria like minimum integrated mean-squared prediction error (IMSPE). Analogues within the coupled GP KOH framework are mostly absent from the literature. Here we derive a novel, closed from IMSPE criteria for sequentially acquiring new simulator data in an active learning setting for KOH. We illustrate how acquisitions space-fill in design space, but concentrate in calibration space. Closed form IMSPE precipitates a closed-form gradient for efficient numerical optimization. We demonstrate that such acquisitions lead to a more efficient simulation campaign on benchmark problems, and conclude with a showcase on a motivating problem involving prediction of equilibrium concentrations of rare earth elements for a liquid-liquid extraction reaction.},
  archiveprefix = {arxiv},
  keywords = {Statistics - Methodology},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\DBC\\KOH\\Koermer_et_al-Active_Learning_for_Simulator_Calibration_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\SMKNCGB9\\2301.html}
}

@article{kohavi1995,
  title = {A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection},
	author = {Kohavi, Ron},
  year = {1995},
  series = {Ijcai},
  volume = {14},
  langid = {english}
}

@article{kopsiaftis2019,
  title = {Gaussian {{Process Regression Tuned}} by {{Bayesian Optimization}} for {{Seawater Intrusion Prediction}}},
	author = {Kopsiaftis, George and Protopapadakis, Eftychios and Voulodimos, Athanasios and Doulamis, Nikolaos and Mantoglou, Aristotelis},
  year = {2019},
  journal = {Computational Intelligence and Neuroscience},
  volume = {2019},
  urldate = {2022-03-04},
  abstract = {Accurate prediction of the seawater intrusion extent is necessary for many applications, such as groundwater management or protection of coastal aquifers from water quality deterioration. However, most applications require a large number of simulations usually at the expense of prediction accuracy. In this study, the Gaussian process regression method is investigated as a potential surrogate model for the computationally expensive variable density model. Gaussian process regression is a nonparametric kernel-based probabilistic model able to handle complex relations between input and output. In this study, the extent of seawater intrusion is represented by the location of the 0.5\,kg/m               3               iso-chlore at the bottom of the aquifer (seawater intrusion toe). The initial position of the toe, expressed as the distance of the specific line from a number of observation points across the coastline, along with the pumping rates are the surrogate model inputs, whereas the final position of the toe constitutes the output variable set. The training sample of the surrogate model consists of 4000 variable density simulations, which differ not only in the pumping rate pattern but also in the initial concentration distribution. The Latin hypercube sampling method is used to obtain the pumping rate patterns. For comparison purposes, a number of widely used regression methods are employed, specifically regression trees and Support Vector Machine regression (linear and nonlinear). A Bayesian optimization method is applied to all the regressors, to maximize their efficiency in the prediction of seawater intrusion. The final results indicate that the Gaussian process regression method, albeit more time consuming, proved to be more efficient in terms of the mean absolute error (MAE), the root mean square error (RMSE), and the coefficient of determination (R2).},
  langid = {english}
}

@article{kovachki,
  title = {Neural {{Operator}}: {{Learning Maps Between Function Spaces With Applications}} to {{PDEs}}},
	author = {Kovachki, Nikola and Li, Zongyi and Liu, Burigede and Azizzadenesheli, Kamyar and Bhattacharya, Kaushik and others},
  abstract = {The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We formulate the neural operator as a composition of linear integral operators and nonlinear activation functions. We prove a universal approximation theorem for our proposed neural operator, showing that it can approximate any given nonlinear continuous operator. The proposed neural operators are also discretization-invariant, i.e., they share the same model parameters among different discretization of the underlying function spaces. Furthermore, we introduce four classes of efficient parameterization, viz., graph neural operators, multi-pole graph neural operators, lowrank neural operators, and Fourier neural operators. An important application for neural operators is learning surrogate maps for the solution operators of partial differential equations (PDEs). We consider standard PDEs such as the Burgers, Darcy subsurface flow, and the Navier-Stokes equations, and show that the proposed neural operators have superior performance compared to existing machine learning based methodologies, while being several orders of magnitude faster than conventional PDE solvers.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\XHQ6JHFZ\Kovachki et al. - Neural Operator Learning Maps Between Function Sp.pdf}
}

@article{kovachki2023,
  title = {Neural Operator: {{Learning}} Maps between Function Spaces with Applications to {{PDEs}}},
	author = {Kovachki, Nikola and Li, Zongyi and Liu, Burigede and Azizzadenesheli, Kamyar and Bhattacharya, Kaushik and others},
  year = {2023},
  journal = {Journal of Machine Learning Research},
  volume = {24},
  number = {89},
  pages = {1--97},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\T3JNKHZH\Kovachki et al. - Neural Operator Learning Maps Between Function Sp.pdf}
}

@article{kovachkia,
  title = {Neural {{Operator}}: {{Learning Maps Between Function Spaces With Applications}} to {{PDEs}}},
	author = {Kovachki, Nikola and Li, Zongyi and Liu, Burigede and Azizzadenesheli, Kamyar and Bhattacharya, Kaushik and others},
  abstract = {The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We formulate the neural operator as a composition of linear integral operators and nonlinear activation functions. We prove a universal approximation theorem for our proposed neural operator, showing that it can approximate any given nonlinear continuous operator. The proposed neural operators are also discretization-invariant, i.e., they share the same model parameters among different discretization of the underlying function spaces. Furthermore, we introduce four classes of efficient parameterization, viz., graph neural operators, multi-pole graph neural operators, lowrank neural operators, and Fourier neural operators. An important application for neural operators is learning surrogate maps for the solution operators of partial differential equations (PDEs). We consider standard PDEs such as the Burgers, Darcy subsurface flow, and the Navier-Stokes equations, and show that the proposed neural operators have superior performance compared to existing machine learning based methodologies, while being several orders of magnitude faster than conventional PDE solvers.},
  langid = {english}
}

@article{krige1951,
  title = {A Statistical Approach to Some Basic Mine Valuation Problems on the {{Witwatersrand}}},
	author = {Krige, Daniel G.},
  year = {1951},
  series = {Chemical, {{Metallurgical}} and {{Mining Society}} of {{South Africa}}},
  langid = {english}
}

@article{kumar2020,
  title = {Active {{Learning Query Strategies}} for {{Classification}}, {{Regression}}, and {{Clustering}}: {{A Survey}}},
  shorttitle = {Active {{Learning Query Strategies}} for {{Classification}}, {{Regression}}, and {{Clustering}}},
	author = {Kumar, Punit and Gupta, Atul},
  year = {2020},
  journal = {Journal of Computer Science and Technology},
  volume = {35},
  number = {4},
  pages = {913--945},
  urldate = {2024-02-05},
  abstract = {Generally, data is available abundantly in unlabeled form, and its annotation requires some cost. The labeling, as well as learning cost, can be minimized by learning with the minimum labeled data instances. Active learning (AL), learns from a few labeled data instances with the additional facility of querying the labels of instances from an expert annotator or oracle. The active learner uses an instance selection strategy for selecting those critical query instances, which reduce the generalization error as fast as possible. This process results in a refined training dataset, which helps in minimizing the overall cost. The key to the success of AL is query strategies that select the candidate query instances and help the learner in learning a valid hypothesis. This survey reviews AL query strategies for classification, regression, and clustering under the pool-based AL scenario. The query strategies under classification are further divided into: informative-based, representative-based, informative- and representative-based, and others. Also, more advanced query strategies based on reinforcement learning and deep learning, along with query strategies under the realistic environment setting, are presented. After a rigorous mathematical analysis of AL strategies, this work presents a comparative analysis of these strategies. Finally, implementation guide, applications, and challenges of AL are discussed.},
  langid = {english},
  keywords = {active classification,active clustering,active learning,active learning query strategy,active regression,deep active learning}
}

@misc{kuntz2022,
  title = {Markov Chains Revisited},
	author = {Kuntz, Juan},
  year = {2022},
  number = {arXiv:2001.02183},
  eprint = {2001.02183},
  primaryclass = {math},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {A rigorous and largely self-contained account of (a) the bread-and-butter concepts and techniques in Markov chain theory and (b) the long-term behaviour of chains. As much as possible, the treatment is probabilistic instead of analytical (I stay away from semigroup theory). Personally, I tend to find that the intuition lies with the former and not the latter. This manuscript is geared towards those interested in the use of Markov chains as models of real-life phenomena. For this reason, I focus on the type of chains most commonly encountered in practice (time-homogeneous, minimal, and right-continuous in the discrete topology) and choose a starting point very familiar to this audience: the (Kendall-) Gillespie Algorithm commonly used to simulate these chains. In order to keep the prerequisite knowledge and technical complications to a minimum, I take a 'bare-bones' approach that keeps the focus on chains (instead of more general processes) to an almost pathological degree: I use the 'jump and hold' structure of chains extensively; almost no martingale theory; minimal coupling; no stochastic calculus; and, even though regeneration and renewal (of course!) feature in the manuscript, they do so exclusively in the context of chains. I have also taken some extra steps to avoid imposing certain assumptions encountered in other texts that sometimes prove to be stumbling blocks in practice (e.g., irreducibility of the state space, boundedness of test functions and of stopping times). For more details, see the preface.},
  archiveprefix = {arxiv},
  keywords = {60J27 (Primary) 60J10 60J22 (Secondary),Mathematics - Probability},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Statistics\\Kuntz-Markov_chains_revisited_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\CF7WJNGF\\2001.html}
}

@techreport{kupresanin2011,
  type = {Technical {{Report}}},
  title = {Comparison of {{Sequential Designs}} of {{Computer Experiments}} in {{High Dimensions}}},
	author = {Kupresanin, A. M. and Johannesson, G.},
  year = {2011},
  number = {LLNL-TR-491692},
  address = {United States},
  institution = {Lawrence Livermore National Lab. (LLNL)},
  abstract = {We continue a long line of research in applying the design and analysis of computer experiments to the study of real world systems. The problem we consider is that of fitting a Gaussian process model for a computer model in applications where the simulation output is a function of a high dimensional input vector. Our computer experiments are designed sequentially as we learn about the model. We perform an empirical comparison of the effectiveness and efficiency of several statistical criteria that have been used in sequential experimental designs. The specific application that motivates this work comes from climatology.},
  langid = {english}
}

@article{kyprioti2020,
  title = {Adaptive Design of Experiments for Global {{Kriging}} Metamodeling through Cross-Validation Information},
	author = {Kyprioti, Aikaterini P. and Zhang, Jize and Taflanidis, Alexandros A.},
  year = {2020},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {62},
  number = {3},
  pages = {1135--1157},
  urldate = {2022-01-02},
  abstract = {This paper discusses a new sequential adaptive design of experiments (DoE) approach for global Kriging metamodeling applications. The sequential implementation is established by using the current metamodel, formulated based on the existing experiments, to guide the selection of the optimal new experiment(s). The score function, defining the DoE objective, combines two components: (1) the metamodel prediction variability, expressed through the predictive variance, and (2) the metamodel bias, approximated through the leave-one-out cross validation (LOOCV) error. The latter is used as a weighting factor to extend traditional DoE approaches that focus solely on the metamodel prediction variability. Two such approaches are considered here, adopting either the integrated mean squared error or the maximum mean squared error as the basic component of the score function. The incorporation of bias information as weighting within these well-established approaches facilitates a direct extension of their respective computational workflows, making the proposed implementation attractive from computational perspective. An efficient optimization scheme for identification of the next experiment, as well as the balancing of exploration and exploitation between the two components of the score function, are also discussed. The incorporation of LOOCV weightings is shown to be highly beneficial in a total of six analytical and engineering examples. Furthermore, these examples demonstrate that for DoE approaches which use LOOCV information as weights, it is preferable to update the predictive variance to explicitly consider the impact of the new experiment, rather than relying strictly on the current metamodel variance.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\Promotion Model Validation\Design of Experiments\Adaptive Methods\Kyprioti_et_al-Adaptive_design_of_experiments_for_global_Kriging_metamodeling_through_2020.pdf}
}

@inproceedings{lakshminarayanan2017,
  title = {Simple and {{Scalable Predictive Uncertainty Estimation}} Using {{Deep Ensembles}}},
  booktitle = {Neural {{Information Processing Systems}} ({{NIPS}})},
	author = {Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles},
  year = {2017},
  pages = {6405--6416},
  urldate = {2022-05-24},
  abstract = {Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs, which learn a distribution over weights, are currently the state-of-the-art for estimating predictive uncertainty; however these require significant modifications to the training procedure and are computationally expensive compared to standard (non-Bayesian) NNs. We propose an alternative to Bayesian NNs that is simple to implement, readily parallelizable, requires very little hyperparameter tuning, and yields high quality predictive uncertainty estimates. Through a series of experiments on classification and regression benchmarks, we demonstrate that our method produces well-calibrated uncertainty estimates which are as good or better than approximate Bayesian NNs. To assess robustness to dataset shift, we evaluate the predictive uncertainty on test examples from known and unknown distributions, and show that our method is able to express higher uncertainty on out-of-distribution examples. We demonstrate the scalability of our method by evaluating predictive uncertainty estimates on ImageNet.},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\IVPDFHGH\\Lakshminarayanan et al. - 2017 - Simple and Scalable Predictive Uncertainty Estimat.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\GDTDB92J\\1612.html}
}

@phdthesis{lam2008,
  title = {Sequential {{Adaptive Design}} in {{Computer Experiments}} for {{Response Surface Model Fit}}},
	author = {Lam, Chen Quin},
  year = {2008},
  langid = {english},
  school = {The Ohio State University},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Lam-Sequential_Adaptive_Design_in_Computer_Experiments_for_Response_Surface_Model_2008.pdf}
}

@article{lammle2023,
  title = {Gradient and Uncertainty Enhanced Sequential Sampling for Global Fit},
	author = {L{\"a}mmle, Sven and Bogoclu, Can and Cremanns, Kevin and Roos, Dirk},
  year = {2023},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {415},
  pages = {116226},
  urldate = {2023-07-29},
  langid = {english},
  keywords = {own},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\IMH\Lammle_et_al-Gradient_and_uncertainty_enhanced_sequential_sampling_for_global_fit_2023.pdf}
}

@article{lampinen2001,
  title = {Bayesian Approach for Neural Networks---Review and Case Studies},
	author = {Lampinen, Jouko and Vehtari, Aki},
  year = {2001},
  journal = {Neural Networks},
  volume = {14},
  number = {3},
  pages = {257--274},
  urldate = {2022-01-21},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Bayesian Neural Networks\Lampinen_Vehtari-Bayesian_approach_for_neural_networks—review_and_case_studies_2001.pdf}
}

@inproceedings{lederer2019,
  title = {Uniform {{Error Bounds}} for {{Gaussian Process Regression}} with {{Application}} to {{Safe Control}}},
  booktitle = {Advances in {{Neural Information Processing Systems}}},
	author = {Lederer, Armin and Umlauft, Jonas and Hirche, Sandra},
  year = {2019},
  volume = {32},
  publisher = {Curran Associates, Inc.},
  urldate = {2024-01-19},
  abstract = {Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure and uniform error bounds have been derived, which allow safe control based on these models. However, existing error bounds require restrictive assumptions. In this paper, we employ the Gaussian process distribution and continuity arguments to derive a novel uniform error bound under weaker assumptions. Furthermore, we demonstrate how this distribution can be used to derive probabilistic Lipschitz constants and analyze the asymptotic behavior of our bound. Finally, we derive safety conditions for the control of unknown dynamical systems based on Gaussian process models and evaluate them in simulations of a robotic manipulator.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\EMPTY_COLLECTION_NAME\Lederer_et_al-Uniform_Error_Bounds_for_Gaussian_Process_Regression_with_Application_to_Safe_2019.pdf}
}

@article{lederer2021,
  title = {Uniform {{Error}} and {{Posterior Variance Bounds}} for {{Gaussian Process Regression}} with {{Application}} to {{Safe Control}}},
	author = {Lederer, Armin and Umlauft, Jonas and Hirche, Sandra},
  year = {2021},
  journal = {arXiv e-prints},
  volume = {arXiv.2101.05328},
  eprint = {2101.05328},
  primaryclass = {cs, eess, stat},
  urldate = {2024-02-05},
  abstract = {In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of performance guarantees using probabilistic model error bounds. To make these approaches applicable in practice, two open challenges must be solved i) Existing error bounds rely on prior knowledge, which might not be available for many real-world tasks. (ii) The relationship between training data and the posterior variance, which mainly drives the error bound, is not well understood and prevents the asymptotic analysis. This article addresses these issues by presenting a novel uniform error bound using Lipschitz continuity and an analysis of the posterior variance function for a large class of kernels. Additionally, we show how these results can be used to guarantee safe control of an unknown dynamical system and provide numerical illustration examples.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Electrical Engineering and Systems Science - Systems and Control,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Lederer_et_al-Uniform_Error_and_Posterior_Variance_Bounds_for_Gaussian_Process_Regression_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\ZIDPBPKC\\2101.html}
}

@article{lee,
  title = {Bayesian {{Statistics}}},
	author = {Lee, Peter M},
  pages = {488},
  langid = {english},
  keywords = {Bayesian},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Lee-Bayesian_Statistics.pdf}
}

@article{lee1980,
  title = {Two Algorithms for Constructing a {{Delaunay}} Triangulation},
	author = {Lee, D. T. and Schachter, B. J.},
  year = {1980},
  journal = {International Journal of Computer \& Information Sciences},
  volume = {9},
  number = {3},
  pages = {219--242},
  urldate = {2022-02-14},
  langid = {english}
}

@book{lee2012,
  title = {Bayesian Statistics: An Introduction},
  shorttitle = {Bayesian Statistics},
	author = {Lee, Peter M.},
  year = {2012},
  edition = {4th},
  publisher = {Wiley},
  abstract = {"- Presents extensive examples throughout the book to complement the theory presented.Includes significant new material on recent techniques such as variational methods, importance sampling, approximate computation and reversible jump MCMC"--},
  lccn = {QA279.5 .L44 2012},
  keywords = {Bayesian statistical decision theory,MATHEMATICS / Probability & Statistics / Bayesian Analysis}
}

@article{lee2019,
  title = {Review of Statistical Model Calibration and Validation---from the Perspective of Uncertainty Structures},
	author = {Lee, Guesuk and Kim, Wongon and Oh, Hyunseok and Youn, Byeng D. and Kim, Nam H.},
  year = {2019},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {60},
  number = {4},
  pages = {1619--1644},
  urldate = {2023-05-10},
  abstract = {Computer-aided engineering (CAE) is now an essential instrument that aids in engineering decision-making. Statistical model calibration and validation has recently drawn great attention in the engineering community for its applications in practical CAE models. The objective of this paper is to review the state-of-the-art and trends in statistical model calibration and validation, based on the available extensive literature, from the perspective of uncertainty structures. After a brief discussion about uncertainties, this paper examines three problem categories---the forward problem, the inverse problem, and the validation problem---in the context of techniques and applications for statistical model calibration and validation.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\GUCIC2LZ\Lee et al. - 2019 - Review of statistical model calibration and valida.pdf}
}

@article{leea,
  title = {Bayesian {{Statistics}}},
	author = {Lee, Peter M},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\EMPTY_COLLECTION_NAME\Lee-Bayesian_Statistics.pdf}
}

@article{lei2018,
  title = {Distribution-{{Free Predictive Inference}} for {{Regression}}},
	author = {Lei, Jing and G'Sell, Max and Rinaldo, Alessandro and Tibshirani, Ryan J. and Wasserman, Larry},
  year = {2018},
  journal = {Journal of the American Statistical Association},
  volume = {113},
  number = {523},
  pages = {1094--1111},
  publisher = {Taylor \& Francis},
  urldate = {2024-01-21},
  abstract = {We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called rank-one-out conformal inference, which has essentially the same computational efficiency as split conformal inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, to adapt to heteroscedasticity in the data. Finally, we propose a model-free notion of variable importance, called leave-one-covariate-out or LOCO inference. Accompanying this article is an R package conformalInference that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.},
  keywords = {Distribution-free,Model misspecification,Prediction band,Regression,Variable importance},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Conformal Prediction\Lei_et_al-Distribution-Free_Predictive_Inference_for_Regression_2018.pdf}
}

@misc{leibfried2022,
  title = {A {{Tutorial}} on {{Sparse Gaussian Processes}} and {{Variational Inference}}},
	author = {Leibfried, Felix and Dutordoir, Vincent and John, S. T. and Durrande, Nicolas},
  year = {2022},
  number = {arXiv:2012.13962},
  eprint = {2012.13962},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-06-15},
  abstract = {Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys a posterior in closed form. However, identifying the posterior GP scales cubically with the number of training examples and requires to store all examples in memory. In order to overcome these obstacles, sparse GPs have been proposed that approximate the true posterior GP with pseudo-training examples. Importantly, the number of pseudo-training examples is user-defined and enables control over computational and memory complexity. In the general case, sparse GPs do not enjoy closed-form solutions and one has to resort to approximate inference. In this context, a convenient choice for approximate inference is variational inference (VI), where the problem of Bayesian inference is cast as an optimization problem -- namely, to maximize a lower bound of the log marginal likelihood. This paves the way for a powerful and versatile framework, where pseudo-training examples are treated as optimization arguments of the approximate posterior that are jointly identified together with hyperparameters of the generative model (i.e. prior and likelihood). The framework can naturally handle a wide scope of supervised learning problems, ranging from regression with heteroscedastic and non-Gaussian likelihoods to classification problems with discrete labels, but also problems with multidimensional labels. The purpose of this tutorial is to provide access to the basic matter for readers without prior knowledge in both GPs and VI. A proper exposition to the subject enables also access to more recent advances (like importance-weighted VI as well as interdomain, multioutput and deep GPs) that can serve as an inspiration for new research ideas.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Leibfried_et_al-A_Tutorial_on_Sparse_Gaussian_Processes_and_Variational_Inference_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\747JYKQF\\2012.html}
}

@article{leone1961,
  title = {The {{Folded Normal Distribution}}},
	author = {Leone, F. C. and Nelson, L. S. and Nottingham, R. B.},
  year = {1961},
  journal = {Technometrics},
  volume = {3},
  number = {4},
  pages = {543--550},
  publisher = {Taylor \& Francis},
  urldate = {2023-12-14},
  abstract = {Measurements are frequently recorded without their algebraic sign. As a consequence, the underlying distribution of measurements is replaced by a distribution of absolute measurements. When the underlying distribution is normal, the resulting distribution is called the ``folded normal distribution''. The authors describe methods for estimating the mean and standard deviation of the normal distribution based on estimates of the mean and standard deviation determined from the folded normal. Tables are provided to assist in the estimation procedure and an example included.}
}

@article{levy2010,
  title = {Computer Experiments: A Review},
  shorttitle = {Computer Experiments},
	author = {Levy, Sigal and Steinberg, David M.},
  year = {2010},
  journal = {AStA Advances in Statistical Analysis},
  volume = {94},
  number = {4},
  pages = {311--324},
  urldate = {2023-06-05},
  abstract = {In this paper we provide a broad introduction to the topic of computer experiments. We begin by briefly presenting a number of applications with different types of output or different goals. We then review modelling strategies, including the popular Gaussian process approach, as well as variations and modifications. Other strategies that are reviewed are based on polynomial regression, non-parametric regression and smoothing spline ANOVA. The issue of multi-level models, which combine simulators of different resolution in the same experiment, is also addressed. Special attention is given to modelling techniques that are suitable for functional data. To conclude the modelling section, we discuss calibration, validation and verification. We then review design strategies including Latin hypercube designs and space-filling designs and their adaptation to computer experiments. We comment on a number of special issues, such as designs for multi-level simulators, nested factors and determination of experiment size.},
  langid = {english},
  keywords = {Deterministic output,Functional data,Gaussian process,Latin hypercube designs,Space filling}
}

@misc{li2021,
  title = {Fourier {{Neural Operator}} for {{Parametric Partial Differential Equations}}},
	author = {Li, Zongyi and Kovachki, Nikola and Azizzadenesheli, Kamyar and Liu, Burigede and Bhattacharya, Kaushik and others},
  year = {2021},
  number = {arXiv:2010.08895},
  eprint = {2010.08895},
  primaryclass = {cs, math},
  publisher = {arXiv},
  urldate = {2023-06-06},
  abstract = {The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. The Fourier neural operator is the first ML-based method to successfully model turbulent flows with zero-shot super-resolution. It is up to three orders of magnitude faster compared to traditional PDE solvers. Additionally, it achieves superior accuracy compared to previous learning-based solvers under fixed resolution.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Mathematics - Numerical Analysis},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Li_et_al-Fourier_Neural_Operator_for_Parametric_Partial_Differential_Equations_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\WLXUY83M\\2010.html}
}

@misc{li2022,
  title = {Physical {{Parameter Calibration}}},
	author = {Li, Yang and Xiong, Shifeng},
  year = {2022},
  number = {arXiv:2208.00124},
  eprint = {2208.00124},
  primaryclass = {math, stat},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on observations. In most real applications, the parameters have specific physical meanings, and we call them physical parameters. To recognize the true underlying physical system, we need to effectively estimate such parameters. However, existing calibration methods cannot do this well due to the model identifiability problem. This paper proposes a semi-parametric model, called the discrepancy decomposition model, to describe the discrepancy between the physical system and the computer model. The proposed model possesses a clear interpretation, and more importantly, it is identifiable under mild conditions. Under this model, we present estimators of the physical parameters and the discrepancy, and then establish their asymptotic properties. Numerical examples show that the proposed method can better estimate the physical parameters than existing methods.},
  archiveprefix = {arxiv},
  keywords = {62P30 62F12,Mathematics - Statistics Theory,Statistics - Methodology},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Statistics\\Bayesian Inference\\Li_Xiong-Physical_Parameter_Calibration_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\A6MXI4ZQ\\2208.html}
}

@article{lin2020,
  title = {Structural Modelling and {{Bayesian}} Inference for Model Validation and Confidence Extrapolation},
	author = {Lin, Shenglin and Li, Wei and Ma, Ping and Yang, Ming},
  year = {2020},
  journal = {Journal of Statistical Computation and Simulation},
  volume = {90},
  number = {2},
  pages = {211--233},
  publisher = {Taylor \& Francis},
  urldate = {2023-09-21},
  abstract = {The hierarchical validation is recommended for assessing the confidence of the large-scale simulation model, through comparing the model predictions with experimental observations at each level. However, the system-level experimental observations may be scarce in the full-scale testing. A new structural modelling approach is proposed to implement the higher-level model validation using lower-level data. The proposed approach relates the computation model to corresponding system responses and lower-level outputs to higher-level responses. Bayesian network with Markov chain Monte Carlo (MCMC) sampling is used to represent the relationship sets and estimate the structural modelling parameters and input variables. Highest posterior density (HPD) confidence range is employed to quantify the model credibility, the confidence intervals of model errors, and the effect of lower-level data on the higher-level model assessment. The proposed methodology is implemented for hierarchical model validation and confidence extrapolation of a guidance model on a flight vehicle using time series data.},
  keywords = {Bayesian network,HPD confidence range,MCMC sampling,Model validation,structural modelling}
}

@inproceedings{lin2021,
  title = {Locally {{Valid}} and {{Discriminative Prediction Intervals}} for {{Deep Learning Models}}},
  booktitle = {Advances in {{Neural Information Processing Systems}}},
	author = {Lin, Zhen and Trivedi, Shubhendu and Sun, Jimeng},
  year = {2021},
  volume = {34},
  pages = {8378--8391},
  publisher = {Curran Associates, Inc.},
  urldate = {2024-01-10},
  abstract = {Crucial for building trust in deep learning models for critical real-world applications is efficient and theoretically sound uncertainty quantification, a task that continues to be challenging. Useful uncertainty information is expected to have two key properties: It should be valid (guaranteeing coverage) and discriminative (more uncertain when the expected risk is high). Moreover, when combined with deep learning (DL) methods, it should be scalable and affect the DL model performance minimally. Most existing Bayesian methods lack frequentist coverage guarantees and usually affect model performance. The few available frequentist methods are rarely discriminative and/or violate coverage guarantees due to unrealistic assumptions. Moreover, many methods are expensive or require substantial modifications to the base neural network. Building upon recent advances in conformal prediction [13, 33] and leveraging the classical idea of kernel regression, we propose Locally Valid and Discriminative prediction intervals (LVD), a simple, efficient, and lightweight method to construct discriminative prediction intervals (PIs) for almost any DL model. With no assumptions on the data distribution, such PIs also offer finite-sample local coverage guarantees (contrasted to the simpler marginal coverage). We empirically verify, using diverse datasets, that besides being the only locally valid method for DL, LVD also exceeds or matches the performance (including coverage rate and prediction accuracy) of existing uncertainty quantification methods, while offering additional benefits in scalability and flexibility.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Conformal Prediction\Lin_et_al-Locally_Valid_and_Discriminative_Prediction_Intervals_for_Deep_Learning_Models_2021.pdf}
}

@misc{lin2022,
  title = {Preference {{Exploration}} for {{Efficient Bayesian Optimization}} with {{Multiple Outcomes}}},
	author = {Lin, Zhiyuan Jerry and Astudillo, Raul and Frazier, Peter I. and Bakshy, Eytan},
  year = {2022},
  number = {arXiv:2203.11382},
  eprint = {2203.11382},
  primaryclass = {cs, math, stat},
  publisher = {arXiv},
  urldate = {2023-05-18},
  abstract = {We consider Bayesian optimization of expensive-to-evaluate experiments that generate vector-valued outcomes over which a decision-maker (DM) has preferences. These preferences are encoded by a utility function that is not known in closed form but can be estimated by asking the DM to express preferences over pairs of outcome vectors. To address this problem, we develop Bayesian optimization with preference exploration, a novel framework that alternates between interactive real-time preference learning with the DM via pairwise comparisons between outcomes, and Bayesian optimization with a learned compositional model of DM utility and outcomes. Within this framework, we propose preference exploration strategies specifically designed for this task, and demonstrate their performance via extensive simulation studies.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Mathematics - Optimization and Control,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Optimization\\BO\\Lin_et_al-Preference_Exploration_for_Efficient_Bayesian_Optimization_with_Multiple_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\T5QR8L9C\\2203.html}
}

@book{link2010,
  title = {Bayesian Inference: With Ecological Applications},
  shorttitle = {Bayesian Inference},
	author = {Link, William August and Barker, Richard J.},
  year = {2010},
  edition = {1st ed},
  publisher = {Elsevier/Academic},
  address = {Amsterdam Boston London},
  abstract = {This text is written to provide a mathematically sound but accessible and engaging introduction to Bayesian inference specifically for environmental scientists, ecologists and wildlife biologists. It emphasizes the power and usefulness of Bayesian methods in an ecological context. The advent of fast personal computers and easily available software has simplified the use of Bayesian and hierarchical models . One obstacle remains for ecologists and wildlife biologists, namely the near absence of Bayesian texts written specifically for them. The book includes many relevant examples, is supported by software and examples on a companion website and will become an essential grounding in this approach for students and research ecologists. . Engagingly written text specifically designed to demystify a complex subject . Examples drawn from ecology and wildlife research . An essential grounding for graduate and research ecologists in the increasingly prevalent Bayesian approach to inference . Companion website with analytical software and examples . Leading authors with world-class reputations in ecology and biostatistics},
  langid = {english},
  lccn = {519.542},
  keywords = {Bayesian},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Bayesian Inference\Link_Barker-Bayesian_inference_2010.pdf}
}

@article{liu2008,
  title = {A {{Bayesian}} Analysis of the Thermal Challenge Problem},
	author = {Liu, F. and Bayarri, M.J. and Berger, J.O. and Paulo, R. and Sacks, J.},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2457--2466},
  urldate = {2021-09-07},
  abstract = {A major question for the application of computer models is Does the computer model adequately represent reality? Viewing the computer models as a potentially biased representation of reality, Bayarri et al. (2007) develop the Simulator Assessment and Validation Engine (SAVE) method as a general framework for answering this question. In this paper, we apply the SAVE method to the challenge problem which involves a thermal computer model designed for certain devices. We develop a statement of confidence that the devices modeled can be applied in intended situations.},
  langid = {english},
  keywords = {Bayesian,Model Validation,Sandia Workshop},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\ValidationWS Sandia Lab\Liu_et_al-A_Bayesian_analysis_of_the_thermal_challenge_problem_2008.pdf}
}

@article{liu2011,
  title = {Toward a {{Better Understanding}} of {{Model Validation Metrics}}},
	author = {Liu, Yu and Chen, Wei and Arendt, Paul and Huang, Hong-Zhong},
  year = {2011},
  journal = {Journal of Mechanical Design},
  volume = {133},
  number = {7},
  urldate = {2021-09-07},
  abstract = {Model validation metrics have been developed to provide a quantitative measure that characterizes the agreement between predictions and observations. In engineering design, the metrics become useful for model selection when alternative models are being considered. Additionally, the predictive capability of a computational model needs to be assessed before it is used in engineering analysis and design. Due to the various sources of uncertainties in both computer simulations and physical experiments, model validation must be conducted based on stochastic characteristics. Currently there is no unified validation metric that is widely accepted. In this paper, we present a classification of validation metrics based on their key characteristics along with a discussion of the desired features. Focusing on stochastic validation with the consideration of uncertainty in both predictions and physical experiments, four main types of metrics, namely classical hypothesis testing, Bayes factor, frequentist's metric, and area metric, are examined to provide a better understanding of the pros and cons of each. Using mathematical examples, a set of numerical studies are designed to answer various research questions and study how sensitive these metrics are with respect to the experimental data size, the uncertainty from measurement error, and the uncertainty in unknown model parameters. The insight gained from this work provides useful guidelines for choosing the appropriate validation metric in engineering applications.},
  langid = {english},
  keywords = {Area Metric,Bayes Faktor,Frequentists Metric,Hypothesis Testing,Model Validation,To Implement,U-Pooling,Validation Metric},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Liu_et_al-Toward_a_Better_Understanding_of_Model_Validation_Metrics_2011.pdf}
}

@article{liu2015,
  title = {An {{Adaptive Bayesian Sequential Sampling Approach}} for {{Global Metamodeling}}},
	author = {Liu, Haitao and Xu, Shengli and Ma, Ying and Chen, Xudong and Wang, Xiaofang},
  year = {2015},
  journal = {Journal of Mechanical Design},
  volume = {138},
  number = {1},
  urldate = {2022-03-04},
  abstract = {Computer simulations have been increasingly used to study physical problems in various fields. To relieve computational budgets, the cheap-to-run metamodels, constructed from finite experiment points in the design space using the design of computer experiments (DOE), are employed to replace the costly simulation models. A key issue related to DOE is designing sequential computer experiments to achieve an accurate metamodel with as few points as possible. This article investigates the performance of current Bayesian sampling approaches and proposes an adaptive maximum entropy (AME) approach. In the proposed approach, the leave-one-out (LOO) cross-validation error estimates the error information in an easy way, the local space-filling exploration strategy avoids the clustering problem, and the search pattern from global to local improves the sampling efficiency. A comparison study of six examples with different types of initial points demonstrated that the AME approach is very promising for global metamodeling.},
  langid = {english}
}

@article{liu2017,
  title = {An Adaptive Sampling Approach for {{Kriging}} Metamodeling by Maximizing Expected Prediction Error},
	author = {Liu, Haitao and Cai, Jianfei and Ong, Yew-Soon},
  year = {2017},
  journal = {Computers \& Chemical Engineering},
  volume = {106},
  pages = {171--182},
  urldate = {2022-01-02},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Liu_et_al-An_adaptive_sampling_approach_for_Kriging_metamodeling_by_maximizing_expected_2017.pdf}
}

@article{liu2018,
  title = {A Survey of Adaptive Sampling for Global Metamodeling in Support of Simulation-Based Complex Engineering Design},
	author = {Liu, Haitao and Ong, Yew-Soon and Cai, Jianfei},
  year = {2018},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {57},
  number = {1},
  pages = {393--416},
  urldate = {2022-03-16},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Liu_et_al-A_survey_of_adaptive_sampling_for_global_metamodeling_in_support_of_2018.pdf}
}

@article{liu2018a,
  title = {A Survey of Adaptive Sampling for Global Metamodeling in Support of Simulation-Based Complex Engineering Design},
	author = {Liu, Haitao and Ong, Yew-Soon and Cai, Jianfei},
  year = {2018},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {57},
  number = {1},
  pages = {393--416},
  urldate = {2023-06-05},
  abstract = {Metamodeling is becoming a rather popular means to approximate the expensive simulations in today's complex engineering design problems since accurate metamodels can bring in a lot of benefits. The metamodel accuracy, however, heavily depends on the locations of the observed points. Adaptive sampling, as its name suggests, places more points in regions of interest by learning the information from previous data and metamodels. Consequently, compared to traditional space-filling sampling approaches, adaptive sampling has great potential to build more accurate metamodels with fewer points (simulations), thereby gaining increasing attention and interest by both practitioners and academicians in various fields. Noticing that there is a lack of reviews on adaptive sampling for global metamodeling in the literature, which is needed, this article categorizes, reviews, and analyzes the state-of-the-art single-/multi-response adaptive sampling approaches for global metamodeling in support of simulation-based engineering design. In addition, we also review and discuss some important issues that affect the success of an adaptive sampling approach as well as providing brief remarks on adaptive sampling for other purposes. Last, challenges and future research directions are provided and discussed.},
  langid = {english},
  keywords = {Adaptive sampling,Global metamodeling,Simulation-based engineering design}
}

@misc{liu2019,
  title = {Accurate {{Uncertainty Estimation}} and {{Decomposition}} in {{Ensemble Learning}}},
	author = {Liu, Jeremiah Zhe and Paisley, John and Kioumourtzoglou, Marianthi-Anna and Coull, Brent},
  year = {2019},
  number = {arXiv:1911.04061},
  eprint = {1911.04061},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {Ensemble learning is a standard approach to building machine learning systems that capture complex phenomena in real-world data. An important aspect of these systems is the complete and valid quantification of model uncertainty. We introduce a Bayesian nonparametric ensemble (BNE) approach that augments an existing ensemble model to account for different sources of model uncertainty. BNE augments a model's prediction and distribution functions using Bayesian nonparametric machinery. It has a theoretical guarantee in that it robustly estimates the uncertainty patterns in the data distribution, and can decompose its overall predictive uncertainty into distinct components that are due to different sources of noise and error. We show that our method achieves accurate uncertainty estimates under complex observational noise, and illustrate its real-world utility in terms of uncertainty decomposition and model bias detection for an ensemble in predict air pollution exposures in Eastern Massachusetts, USA.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Uncertainty Quantification\\Liu_et_al-Accurate_Uncertainty_Estimation_and_Decomposition_in_Ensemble_Learning_2019.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\IS3SMKGF\\1911.html}
}

@article{loeppky2009,
  title = {Choosing the {{Sample Size}} of a {{Computer Experiment}}: {{A Practical Guide}}},
  shorttitle = {Choosing the {{Sample Size}} of a {{Computer Experiment}}},
	author = {Loeppky, Jason L. and Sacks, Jerome and Welch, William J.},
  year = {2009},
  journal = {Technometrics},
  volume = {51},
  number = {4},
  pages = {366--376},
  urldate = {2022-02-20},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Loeppky_et_al-Choosing_the_Sample_Size_of_a_Computer_Experiment_2009.pdf}
}

@inproceedings{lorenz1956,
  title = {Empirical Orthogonal Functions and Statistical Weather Prediction},
	author = {Lorenz, E.N},
  year = {1956},
  series = {Scientific {{Report}} 1, {{Statistical Forecasting Project}}},
  publisher = {MIT},
  address = {Cambridge}
}

@inproceedings{loshchilov2017,
  title = {{{SGDR}}: {{Stochastic Gradient Descent}} with {{Warm Restarts}}},
  shorttitle = {{{SGDR}}},
  booktitle = {5th {{International Conference}} on {{Learning Representations}}},
	author = {Loshchilov, Ilya and Hutter, Frank},
  year = {2017},
  urldate = {2024-02-08},
  abstract = {Restart techniques are common in gradient-free optimization to deal with multimodal functions. Partial warm restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions. In this paper, we propose a simple warm restart technique for stochastic gradient descent to improve its anytime performance when training deep neural networks. We empirically study its performance on the CIFAR-10 and CIFAR-100 datasets, where we demonstrate new state-of-the-art results at 3.14\% and 16.21\%, respectively. We also demonstrate its advantages on a dataset of EEG recordings and on a downsampled version of the ImageNet dataset. Our source code is available at https://github.com/loshchil/SGDR},
  keywords = {Computer Science - Machine Learning,Computer Science - Neural and Evolutionary Computing,Mathematics - Optimization and Control},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Optimization\\Loshchilov_Hutter-SGDR_2017.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\NZZ9LRVF\\1608.html}
}

@article{lu2021,
  title = {Strategies for Sequential Design of Experiments and Augmentation},
	author = {Lu, Lu and {Anderson-Cook}, Christine M.},
  year = {2021},
  journal = {Quality and Reliability Engineering International},
  volume = {37},
  number = {5},
  pages = {1740--1757},
  urldate = {2023-06-05},
  abstract = {The benefits of sequential design of experiments have long been described for both model-based and space-filling designs. However, in our experience, too few practitioners take advantage of the opportunity afforded by this approach to maximize the learning from their experimentation. By obtaining data sequentially, it is possible to learn from the early stages to inform subsequent data collection, minimize wasted resources, and provide answers for a series of objectives for the overall experiment. This paper provides methods and algorithms to create augmented distance-based space-filling designs, using both uniform and non-uniform space-filling strategies, that can be constructed at each stage based on information learned in earlier stages. We illustrate the methods with several examples that involve different initial data, types of space-filing designs and experimental goals.},
  copyright = {{\copyright} 2020 John Wiley \& Sons Ltd.},
  langid = {english},
  keywords = {augmented designs,augmented USF designs,maximin distance criterion,non-uniform space-filling (NUSF) designs | uniform space-filling (USF) designs |augmented NUSF designs,weighted distance criterion},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\AJU5962N\qre.html}
}

@article{lu2021a,
  title = {{{DeepONet}}: {{Learning}} Nonlinear Operators for Identifying Differential Equations Based on the Universal Approximation Theorem of Operators},
  shorttitle = {{{DeepONet}}},
	author = {Lu, Lu and Jin, Pengzhan and Karniadakis, George Em},
  year = {2021},
  journal = {Nature Machine Intelligence},
  volume = {3},
  number = {3},
  eprint = {1910.03193},
  primaryclass = {cs, stat},
  pages = {218--229},
  urldate = {2023-06-06},
  abstract = {While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear continuous operator. This universal approximation theorem is suggestive of the potential application of neural networks in learning nonlinear operators from data. However, the theorem guarantees only a small approximation error for a sufficient large network, and does not consider the important optimization and generalization errors. To realize this theorem in practice, we propose deep operator networks (DeepONets) to learn operators accurately and efficiently from a relatively small dataset. A DeepONet consists of two sub-networks, one for encoding the input function at a fixed number of sensors \$x\_i, i=1,{\textbackslash}dots,m\$ (branch net), and another for encoding the locations for the output functions (trunk net). We perform systematic simulations for identifying two types of operators, i.e., dynamic systems and partial differential equations, and demonstrate that DeepONet significantly reduces the generalization error compared to the fully-connected networks. We also derive theoretically the dependence of the approximation error in terms of the number of sensors (where the input function is defined) as well as the input function type, and we verify the theorem with computational results. More importantly, we observe high-order error convergence in our computational tests, namely polynomial rates (from half order to fourth order) and even exponential convergence with respect to the training dataset size.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Lu_et_al-DeepONet_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\GWTUK7JE\\1910.html}
}

@article{lu2021b,
  title = {Learning Nonlinear Operators via {{DeepONet}} Based on the Universal Approximation Theorem of Operators},
	author = {Lu, Lu and Jin, Pengzhan and Pang, Guofei and Zhang, Zhongqiang and Karniadakis, George Em},
  year = {2021},
  journal = {Nature Machine Intelligence},
  volume = {3},
  number = {3},
  pages = {218--229},
  publisher = {Nature Publishing Group},
  urldate = {2023-06-12},
  abstract = {It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications.},
  copyright = {2021 The Author(s), under exclusive licence to Springer Nature Limited},
  langid = {english},
  keywords = {Applied mathematics,Computational science},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Lu_et_al-Learning_nonlinear_operators_via_DeepONet_based_on_the_universal_approximation_2021.pdf}
}

@misc{ma2019,
  title = {Variational {{Implicit Processes}}},
	author = {Ma, Chao and Li, Yingzhen and {Hern{\'a}ndez-Lobato}, Jos{\'e} Miguel},
  year = {2019},
  number = {arXiv:1806.02390},
  eprint = {1806.02390},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {We introduce the implicit processes (IPs), a stochastic process that places implicitly defined multivariate distributions over any finite collections of random variables. IPs are therefore highly flexible implicit priors over functions, with examples including data simulators, Bayesian neural networks and non-linear transformations of stochastic processes. A novel and efficient approximate inference algorithm for IPs, namely the variational implicit processes (VIPs), is derived using generalised wake-sleep updates. This method returns simple update equations and allows scalable hyper-parameter learning with stochastic optimization. Experiments show that VIPs return better uncertainty estimates and lower errors over existing inference methods for challenging models such as Bayesian neural networks, and Gaussian processes.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Ma_et_al-Variational_Implicit_Processes_2019.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\MKK4565T\\1806.html}
}

@article{mackay1992,
  title = {A {{Practical Bayesian Framework}} for {{Backpropagation Networks}}},
	author = {MacKay, David J. C.},
  year = {1992},
  journal = {Neural Computation},
  volume = {4},
  number = {3},
  pages = {448--472},
  urldate = {2022-01-21},
  abstract = {A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible (1) objective comparisons between solutions using alternative network architectures, (2) objective stopping rules for network pruning or growing procedures, (3) objective choice of magnitude and type of weight decay terms or additive regularizers (for penalizing large weights, etc.), (4) a measure of the effective number of well-determined parameters in a model, (5) quantified estimates of the error bars on network parameters and on network output, and (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian "evidence" automatically embodies "Occam's razor," penalizing overflexible and overcomplex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalization ability and the Bayesian evidence is obtained.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Bayesian Neural Networks\MacKay-A_Practical_Bayesian_Framework_for_Backpropagation_Networks_1992.pdf}
}

@incollection{mackay1994,
  title = {Automatic Relevance Determination for Neural Networks},
  booktitle = {Technical Report in Preparation.},
	author = {MacKay, David JC and Neal, Radford M},
  year = {1994},
  publisher = {Cambridge University}
}

@inproceedings{macke2000,
  title = {An Adaptive Response Surface Method Utilizing Error Estimates},
  booktitle = {8th {{ASCE Specialty Conference}} on {{Probabilistic Mechanics}} and {{Structural Reliability}}},
	author = {Macke, Michael and Roos, Dirk and Riedel, J{\"o}rg},
  year = {2000}
}

@article{mackman2013,
  title = {Comparison of {{Adaptive Sampling Methods}} for {{Generation}} of {{Surrogate Aerodynamic Models}}},
	author = {Mackman, T. J. and Allen, C. B. and Ghoreyshi, M. and Badcock, K. J.},
  year = {2013},
  journal = {AIAA Journal},
  volume = {51},
  number = {4},
  pages = {797--808},
  urldate = {2022-01-02},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Mackman_et_al-Comparison_of_Adaptive_Sampling_Methods_for_Generation_of_Surrogate_Aerodynamic_2013.pdf}
}

@inproceedings{maddox2021,
  title = {Conditioning {{Sparse Variational Gaussian Processes}} for {{Online Decision-making}}},
  booktitle = {Advances in {{Neural Information Processing Systems}}},
	author = {Maddox, Wesley J and Stanton, Samuel and Wilson, Andrew G},
  year = {2021},
  volume = {34},
  pages = {6365--6379},
  publisher = {Curran Associates, Inc.},
  urldate = {2024-01-06},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Maddox_et_al-Conditioning_Sparse_Variational_Gaussian_Processes_for_Online_Decision-making_2021.pdf}
}

@inproceedings{mahadevan2007,
  title = {Model {{Error Quantification}} for {{Reliability-Based Design}}},
  booktitle = {{{SAE World Congress}} \&  {{Exhibition}}},
	author = {Mahadevan, Sankaran and Rebba, Ramesh},
  year = {2007},
  pages = {2007-01-1743},
  urldate = {2023-11-14},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Reliability-based\Mahadevan_Rebba-Model_Error_Quantification_for_Reliability-Based_Design_2007.pdf}
}

@techreport{mahadevan2009,
  title = {Functional Mapping Approach to Incoporate Epistemic Uncertainty in System Reliability Assessment},
	author = {Mahadevan, Sankaran},
  year = {2009},
  abstract = {Enter UU (Unclassified Unlimited) or SAR (Same as Report). An entry in this block is necessary if the abstract is to be limited.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\WAI4MKGE\Mahadevan - Functional mapping approach to incoporate epistemi.pdf}
}

@misc{makarova2021,
  title = {Risk-Averse {{Heteroscedastic Bayesian Optimization}}},
	author = {Makarova, Anastasiia and Usmanova, Ilnura and Bogunovic, Ilija and Krause, Andreas},
  year = {2021},
  number = {arXiv:2111.03637},
  eprint = {2111.03637},
  primaryclass = {cs},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {Many black-box optimization tasks arising in high-stakes applications require risk-averse decisions. The standard Bayesian optimization (BO) paradigm, however, optimizes the expected value only. We generalize BO to trade mean and input-dependent variance of the objective, both of which we assume to be unknown a priori. In particular, we propose a novel risk-averse heteroscedastic Bayesian optimization algorithm (RAHBO) that aims to identify a solution with high return and low noise variance, while learning the noise distribution on the fly. To this end, we model both expectation and variance as (unknown) RKHS functions, and propose a novel risk-aware acquisition function. We bound the regret for our approach and provide a robust rule to report the final decision point for applications where only a single solution must be identified. We demonstrate the effectiveness of RAHBO on synthetic benchmark functions and hyperparameter tuning tasks.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Optimization\\BO\\Makarova_et_al-Risk-averse_Heteroscedastic_Bayesian_Optimization_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\PLGZ858J\\2111.html}
}

@phdthesis{manokhin2022,
  title = {Machine {{Learning}} for {{Probabilistic Prediction}}},
	author = {Manokhin, Valery},
  year = {2022},
  abstract = {Prediction is the key objective of many machine learning applications. Accurate, reliable and robust predictions are essential for optimal and fair decisions by downstream components of artificial intelligence systems, especially in high-stakes applications, such as personalised health, self-driving cars, finance, new drug development, forecasting of election outcomes and pandemics.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\YA5BTSBV\Manokhin - Machine Learning for Probabilistic Prediction.pdf}
}

@article{marmin2022,
  title = {Deep {{Gaussian Processes}} for {{Calibration}} of {{Computer Models}} (with {{Discussion}})},
	author = {Marmin, S{\'e}bastien and Filippone, Maurizio},
  year = {2022},
  journal = {Bayesian Analysis},
  volume = {17},
  number = {4},
  pages = {1301--1350},
  publisher = {International Society for Bayesian Analysis},
  urldate = {2023-05-10},
  abstract = {Bayesian calibration of black-box computer models offers an established framework for quantification of uncertainty of model parameters and predictions. Traditional Bayesian calibration involves the emulation of the computer model and an additive model discrepancy term using Gaussian processes; inference is then carried out using Markov chain Monte Carlo. This calibration approach is limited by the poor scalability of Gaussian processes and by the need to specify a sensible covariance function to deal with the complexity of the computer model and the discrepancy. In this work, we propose a novel calibration framework, where these challenges are addressed by means of compositions of Gaussian processes into Deep Gaussian processes and scalable variational inference techniques. Thanks to this formulation, it is possible to obtain a flexible calibration approach, which is easy to implement in development environments featuring automatic differentiation and exploiting GPU-type hardware. We show how our proposal yields a powerful alternative to the state-of-the-art by means of experimental validations on various calibration problems. We conclude the paper by showing how we can carry out adaptive experimental design, and by discussing the identifiability properties of the proposed calibration model.},
  keywords = {62F15,62K99,62M45,Bayesian inference,computer experiments,deep Gaussian process,Neural nets},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\DBC\KOH\Marmin_Filippone-Deep_Gaussian_Processes_for_Calibration_of_Computer_Models_(with_Discussion)_2022.pdf}
}

@misc{martinabadi2015,
  title = {{{TensorFlow}}: {{Large-Scale Machine Learning}} on {{Heterogeneous Systems}}},
	author = {{Mart{\'i}n Abadi} and {Ashish Agarwal} and {Paul Barham} and {Eugene Brevdo} and {Zhifeng Chen} and others},
  year = {2015}
}

@book{matern1986,
  title = {Spatial {{Variation}}},
	author = {Mat{\'e}rn, Bertil},
  year = {1986},
  series = {Lecture {{Notes}} in {{Statistics}}},
  edition = {2},
  publisher = {Springer},
  address = {New York},
  urldate = {2022-01-21},
  langid = {english}
}

@article{mattis2015,
  title = {Parameter Estimation and Prediction for Groundwater Contamination Based on Measure Theory},
	author = {Mattis, S. A. and Butler, T. D. and Dawson, C. N. and Estep, D. and Vesselinov, V. V.},
  year = {2015},
  journal = {Water Resources Research},
  volume = {51},
  number = {9},
  pages = {7608--7629},
  urldate = {2023-07-28},
  abstract = {The problem of groundwater contamination in an aquifer is one with many uncertainties. Properly quantifying these uncertainties is essential in order to make reliable probabilistic-based predictions and decisions regarding remediation strategies. In this work, a measure-theoretic framework is employed to quantify uncertainties in a simplified groundwater contamination transport model. Given uncertain data from observation wells, the stochastic inverse problem is solved numerically to obtain a probability measure on the space of unknown model parameters characterizing groundwater flow and contaminant transport in an aquifer, as well as unknown model boundary or source terms such as the contaminant source release into the environment. This probability measure is used to make predictions of future contaminant concentrations and to analyze possible remediation techniques. The ability to identify regions of small but nonzero probability using this method is illustrated.},
  copyright = {{\copyright} 2015. American Geophysical Union. All Rights Reserved.},
  langid = {english},
  keywords = {contaminant transport,groundwater,measure theory,parameter estimation},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\PushForward Inference\Mattis_et_al-Parameter_estimation_and_prediction_for_groundwater_contamination_based_on_2015.pdf}
}

@article{mattis2022,
  title = {Learning {{Quantities}} of {{Interest}} from Dynamical Systems for Observation-Consistent Inversion},
	author = {Mattis, S. A. and Steffen, K. R. and Butler, T. and Dawson, C. N. and Estep, D.},
  year = {2022},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {388},
  pages = {114230},
  urldate = {2023-07-28},
  abstract = {Dynamical systems arise in a wide variety of mathematical models from the physical, engineering, life, and social sciences. A common challenge is to quantify uncertainties on model inputs (i.e., parameters) that correspond to a quantitative characterization of uncertainties on observable Quantities of Interest (QoI). To this end, we consider a stochastic inverse problem (SIP) with a solution described by a pullback probability measure. This is referred to as an observation-consistent solution since its subsequent push-forward through the QoI map matches the observed probability distribution on model outputs. A distinction is made between QoI useful for solving the SIP and arbitrary model output data. In dynamical systems, model output data are often given as a series of state variable responses recorded over a particular time window. Consequently, the dimension of output data can easily exceed O(1E4) or more due to the frequency of observations, and the correct choice or construction of a QoI from this data is not self-evident. We present a new framework, Learning Uncertain Quantities (LUQ), that facilitates the tractable solution of SIPs for dynamical systems. Given ensembles of predicted (simulated) time series and (noisy) observed data, LUQ provides routines for filtering data, learning the underlying dynamics in an unsupervised manner, classifying the observations, and performing feature extraction to learn the QoI map. Subsequently, time series data are transformed into samples coming from the underlying predicted and observed distributions associated with the QoI so that solutions to the SIP are computable. Following the introduction and demonstration of LUQ, numerical results from several SIPs are presented for a variety of dynamical systems arising in the life and physical sciences. In the interest of scientific reproducibility, we provide links to our Python implementation of LUQ, as well as all data and scripts required to reproduce the results in this manuscript.},
  langid = {english},
  keywords = {Dynamical systems,Observation-consistent,Quantity of Interest,Stochastic inverse problems,Uncertainty quantification},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\PushForward Inference\\Mattis_et_al-Learning_Quantities_of_Interest_from_dynamical_systems_for_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\9P34KHN3\\S0045782521005582.html}
}

@article{maupin2019,
  title = {Validation {{Metrics}} for {{Deterministic}} and {{Probabilistic Data}}},
	author = {Maupin, Kathryn A and Box, P O and Porter, Nathan W and Drive, Stinson},
  year = {2019},
  pages = {18},
  abstract = {Computational modeling and simulation are paramountto modern science. Computational models often replace physical experimentsthat are prohibitively expensive,dangerous,or occur at extreme scales. Thus,it is critical that these models accurately represent and can be used as replacements for reality. This paper provides an analysis of metrics that may be used to determine the validity of a computational model. While some metrics have a direct physical meaning and a long history of use, others, especially those that compare probabilistic data, are more difficult to interpret. Furthermore, the process of model validation is often application-specific, making the procedure itselfchallenging and the results difficultto defend. We therefore provide guidance and recommendations as to which validation metric to use, as well as how to use and decipher the results. An example is included that compares interpretations ofvarious metrics and demonstrates the impact ofmodel and experimental uncertainty on validation processes.},
  langid = {english},
  keywords = {Model Validation,To Implement,Validation Metric},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Maupin_et_al-Validation_Metrics_for_Deterministic_and_Probabilistic_Data_2019.pdf}
}

@article{maupin2020,
  title = {Model Discrepancy Calibration across Experimental Settings},
	author = {Maupin, Kathryn A. and Swiler, Laura P.},
  year = {2020},
  journal = {Reliability Engineering \& System Safety},
  volume = {200},
  pages = {106818},
  urldate = {2023-05-10},
  abstract = {Despite continuing advances in the reliability of computational modeling and simulation, model inadequacy remains a pervasive concern across scientific disciplines. Further challenges are introduced into the already complex problem of ``correcting'' an inadequate model when experimental data is collected at varying experimental settings. This paper introduces a general approach to calibrating a model discrepancy function when the model is expected to perform for multiple experimental configurations and give predictions as a function of temporal and/or spatial coordinates.},
  langid = {english},
  keywords = {Bayes' Rule,Computational modeling,Inverse problems,Model discrepancy,Model form error,Model inadequacy},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\DBC\\KOH\\Maupin_Swiler-Model_discrepancy_calibration_across_experimental_settings_2020.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\I5ZIMHGF\\S0951832019301802.html}
}

@phdthesis{mcfarland2008,
  title = {Uncertainty {{Analysis}} for {{Computer Simulations}} Trough {{Validation}} and {{Calibration}}},
	author = {McFarland, John Milburn},
  year = {2008},
  address = {Nashville, Tennessee},
  langid = {english},
  school = {Vanderbilt University},
  keywords = {Model Calibration,Model Validation,Uncertainty,Uncertainty Quantification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\General\McFarland-UNCERTAINTY_ANALYSIS_FOR_COMPUTER_SIMULATIONS_THROUGH_VALIDATION_AND_CALIBRATION_2008.pdf}
}

@article{mckay1979,
  title = {A {{Comparison}} of {{Three Methods}} for {{Selecting Values}} of {{Input Variables}} in the {{Analysis}} of {{Output}} from a {{Computer Code}}},
	author = {McKay, M. D. and Beckman, R. J. and Conover, W. J.},
  year = {1979},
  journal = {Technometrics},
  volume = {21},
  number = {2},
  eprint = {1268522},
  eprinttype = {jstor},
  pages = {239},
  urldate = {2022-02-14}
}

@book{meeker1998,
  title = {Statistical Methods for Reliability Data},
	author = {Meeker, William Q. and Escobar, Luis A. and Pascual, Francis G.},
  year = {1998},
  series = {Wiley Series in Probability and Statistics},
  publisher = {Wiley},
  abstract = {"This book improves Meeker and Escobar (1998, Wiley) not only in terms of organization and presentation, but also in extensions and modifications to the technical material. It presents state-of-the-art, computer-based statistical methods for reliability data analysis and for test planning of industrial products. It also improves long time established techniques as it demonstrates how to apply the new graphical, numerical, or simulation-based methods to a broad range of models encountered in reliability data analysis. Bayesian methods in solving practical problems (e.g. models involving random effects or censoring that arises in reliability studies) are now incorporated where appropriate; the computations are done with WinBUGS. Ample exercises that extend and strengthen the concepts in the book are included. The criterion for integrating material in the book is that the authors have in-hand or have seen real applications for the methodology. The book is specifically geared for a one-semester course on the topic in either a statistics or engineering department at either the upper-undergraduate or beginning graduate levels. R functions and subroutines, along with an extensive list of data sets, are included on a massive web site that is meticulously maintained by the authors"--},
  keywords = {Reliability (Engineering),Statistical methods},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Lifetime Coffin Manson\Meeker_et_al-Statistical_methods_for_reliability_data_2022.pdf}
}

@article{metropolis,
  title = {Equation of {{State Calculations}} by {{Fast Computing Machines}}},
	author = {Metropolis, Nicholas and Rosenbluth, Arianna W and Rosenbluth, Marshall N and Teller, Augusta H},
  pages = {7},
  langid = {english},
  keywords = {MCMC},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Metropolis_et_al-Equation_of_State_Calculations_by_Fast_Computing_Machines.pdf}
}

@book{meyer1991,
  title = {Computer {{Simulation}} in {{Materials Science}}: {{Interatomic Potentials}}, {{Simulation Techniques}} and {{Applications}}},
  shorttitle = {Computer {{Simulation}} in {{Materials Science}}},
	author = {Meyer, Madeleine and Pontikis, Vassilis},
  year = {1991},
  series = {{{NATO Science Series E}}},
  edition = {1},
  volume = {205},
  publisher = {Springer Dordrecht},
  langid = {english}
}

@inproceedings{mi2013,
  title = {The Life Prediction of Lead-Free Solder Joint with Type-{{I}} Interval Censored Data},
  booktitle = {2013 {{International Conference}} on {{Quality}}, {{Reliability}}, {{Risk}}, {{Maintenance}}, and {{Safety Engineering}} ({{QR2MSE}})},
	author = {Mi, Jinhua and Wang, Jie and Li, Yan-Feng and Huang, Hong-Zhong and Yang, Yuan-Jian and others},
  year = {2013},
  pages = {904--907},
  abstract = {By collecting the data from thermal cycling test of an lead-free BGA interconnection structure, using type-I interval censored data processing method and modified Emgelmaier fatigue life model, the cycles to failure of lead-free solder joint are predicted. The comparison between the results obtained by proposed methods and the life calculated by Matlab verifies the practicability and effectiveness of the two methods.},
  keywords = {Data models,Data processing,Fatigue,fatigue life prediction,Lead,lead-free solider joint,Mathematical model,Reliability,Soldering,thermal cycling test,type-I interval censored data},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\6D8L2PPD\6625714.html}
}

@book{michalewicz1992,
  title = {{Genetic Algorithms + Data Structures = Evolution Programs}},
	author = {Michalewicz, Zbigniew},
  year = {1992},
  edition = {3},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  urldate = {2022-01-20},
  langid = {german}
}

@article{mishra2006,
  title = {Some {{New Test Functions}} for {{Global Optimization}} and {{Performance}} of {{Repulsive Particle Swarm Method}}},
	author = {Mishra, S. K.},
  year = {2006},
  journal = {SSRN Electronic Journal},
  urldate = {2022-01-20},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Benchmarkfunctions\Mishra-Some_New_Test_Functions_for_Global_Optimization_and_Performance_of_Repulsive_2006.pdf}
}

@article{mo2017,
  title = {A {{Taylor Expansion}}-{{Based Adaptive Design Strategy}} for {{Global Surrogate Modeling With Applications}} in {{Groundwater Modeling}}},
	author = {Mo, Shaoxing and Lu, Dan and Shi, Xiaoqing and Zhang, Guannan and Ye, Ming and others},
  year = {2017},
  journal = {Water Resources Research},
  volume = {53},
  number = {12},
  urldate = {2022-01-02},
  abstract = {Global sensitivity analysis (GSA) and uncertainty quantification (UQ) for groundwater modeling are challenging because of the model complexity and significant computational requirements. To reduce the massive computational cost, a cheap-to-evaluate surrogate model is usually constructed to approximate and replace the expensive groundwater models in the GSA and UQ. Constructing an accurate surrogate requires actual model simulations on a number of parameter samples. Thus, a robust experimental design strategy is desired to locate informative samples so as to reduce the computational cost in surrogate construction and consequently to improve the efficiency in the GSA and UQ. In this study, we develop a Taylor expansion-based adaptive design (TEAD) that aims to build an accurate global surrogate model with a small training sample size. TEAD defines a novel hybrid score function to search informative samples, and a robust stopping criterion to terminate the sample search that guarantees the resulted approximation errors satisfy the desired accuracy. The good performance of TEAD in building global surrogate models is demonstrated in seven analytical functions with different dimensionality and complexity in comparison to two widely used experimental design methods. The application of the TEAD-based surrogate method in two groundwater models shows that the TEAD design can effectively improve the computational efficiency of GSA and UQ for groundwater modeling.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Mo_et_al-A_Taylor_Expansion‐Based_Adaptive_Design_Strategy_for_Global_Surrogate_Modeling_2017.PDF}
}

@article{mockus1994,
  title = {Application of {{Bayesian}} Approach to Numerical Methods of Global and Stochastic Optimization},
	author = {Mockus, Jonas},
  year = {1994},
  journal = {Journal of Global Optimization},
  volume = {4},
  number = {4},
  pages = {347--365},
  urldate = {2022-09-16},
  langid = {english}
}

@article{mohammadi2021,
  title = {Cross-Validation Based Adaptive Sampling for {{Gaussian}} Process Models},
	author = {Mohammadi, Hossein and Challenor, Peter and Williamson, Daniel and Goodfellow, Marc},
  year = {2021},
  journal = {arXiv:2005.01814},
  eprint = {2005.01814},
  urldate = {2021-09-07},
  abstract = {In many real-world applications, we are interested in approximating black-box, costly functions as accurately as possible with the smallest number of function evaluations. A complex computer code is an example of such a function. In this work, a Gaussian process (GP) emulator is used to approximate the output of complex computer code. We consider the problem of extending an initial experiment (set of model runs) sequentially to improve the emulator. A sequential sampling approach based on leave-one-out (LOO) cross-validation is proposed that can be easily extended to a batch mode. This is a desirable property since it saves the user time when parallel computing is available. After fitting a GP to training data points, the expected squared LOO (ES-LOO) error is calculated at each design point. ES-LOO is used as a measure to identify important data points. More precisely, when this quantity is large at a point it means that the quality of prediction depends a great deal on that point and adding more samples nearby could improve the accuracy of the GP. As a result, it is reasonable to select the next sample where ES-LOO is maximised. However, ES-LOO is only known at the experimental design and needs to be estimated at unobserved points. To do this, a second GP is fitted to the ES-LOO errors and where the maximum of the modified expected improvement (EI) criterion occurs is chosen as the next sample. EI is a popular acquisition function in Bayesian optimisation and is used to trade-off between local/global search. However, it has a tendency towards exploitation, meaning that its maximum is close to the (current) ``best'' sample. To avoid clustering, a modified version of EI, called pseudo expected improvement, is employed which is more explorative than EI yet allows us to discover unexplored regions. Our results show that the proposed sampling method is promising.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Adaptive Sampling,Bayesian Optimization,Design of Experiments,Gaussian processes,Optimization},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Mohammadi_et_al-Cross-validation_based_adaptive_sampling_for_Gaussian_process_models_2021.pdf}
}

@article{moriconi2020,
  title = {High-Dimensional {{Bayesian}} Optimization Using Low-Dimensional Feature Spaces},
	author = {Moriconi, Riccardo and Deisenroth, Marc Peter and Sesh Kumar, K. S.},
  year = {2020},
  journal = {Machine Learning},
  volume = {109},
  number = {9-10},
  pages = {1925--1943},
  urldate = {2022-08-15},
  abstract = {Abstract             Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. However, BO is practically limited to optimizing 10--20 parameters. To scale BO to high dimensions, we usually make structural assumptions on the decomposition of the objective and/or exploit the intrinsic lower dimensionality of the problem, e.g. by using linear projections. We could achieve a higher compression rate with nonlinear projections, but learning these nonlinear embeddings typically requires much data. This contradicts the BO objective of a relatively small evaluation budget. To address this challenge, we propose to learn a low-dimensional feature space jointly with (a) the response surface and (b) a reconstruction mapping. Our approach allows for optimization of BO's acquisition function in the lower-dimensional subspace, which significantly simplifies the optimization problem. We reconstruct the original parameter space from the lower-dimensional subspace for evaluating the black-box function. For meaningful exploration, we solve a constrained optimization problem.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Moriconi_et_al-High-dimensional_Bayesian_optimization_using_low-dimensional_feature_spaces_2020.pdf}
}

@misc{moss2023,
  title = {Inducing {{Point Allocation}} for {{Sparse Gaussian Processes}} in {{High-Throughput Bayesian Optimisation}}},
	author = {Moss, Henry B. and Ober, Sebastian W. and Picheny, Victor},
  year = {2023},
  number = {arXiv:2301.10123},
  eprint = {2301.10123},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-06-15},
  abstract = {Sparse Gaussian Processes are a key component of high-throughput Bayesian Optimisation (BO) loops; however, we show that existing methods for allocating their inducing points severely hamper optimisation performance. By exploiting the quality-diversity decomposition of Determinantal Point Processes, we propose the first inducing point allocation strategy designed specifically for use in BO. Unlike existing methods which seek only to reduce global uncertainty in the objective function, our approach provides the local high-fidelity modelling of promising regions required for precise optimisation. More generally, we demonstrate that our proposed framework provides a flexible way to allocate modelling capacity in sparse models and so is suitable broad range of downstream sequential decision making tasks.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Moss_et_al-Inducing_Point_Allocation_for_Sparse_Gaussian_Processes_in_High-Throughput_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\3YSGJMQQ\\2301.html}
}

@inproceedings{most2006,
  title = {Adaptive Response Surface Approach Using Artificial Neural Networks and {{Moving Least Squares}}},
  booktitle = {17th {{International Conference}} on the {{Applications}} of {{Computer Science}} and {{Mathematics}} in {{Architecture}} and {{Civil Engineering}}},
	author = {Most, Thomas and Bucher, Christian},
  year = {2006},
  address = {Weimar, Germany},
}

@article{most2006a,
  title = {Adaptive Response Surface Approach Using Artificial Neural Networks and {{Moving Least Squares}}},
	author = {{Most} and {Bucher}},
  year = {2006},
  publisher = {Unpublished},
  urldate = {2024-02-07},
  langid = {english}
}

@article{moustapha2022,
  title = {Active Learning for Structural Reliability: {{Survey}}, General Framework and Benchmark},
  shorttitle = {Active Learning for Structural Reliability},
	author = {Moustapha, Maliki and Marelli, Stefano and Sudret, Bruno},
  year = {2022},
  journal = {Structural Safety},
  volume = {96},
  pages = {102174},
  urldate = {2023-02-04},
  abstract = {Active learning methods have recently surged in the literature due to their ability to solve complex structural reliability problems within an affordable computational cost. These methods are designed by adaptively building an inexpensive surrogate of the original limit-state function. Examples of such surrogates include Gaussian process models which have been adopted in many contributions, the most popular ones being the efficient global reliability analysis (EGRA) and the active Kriging Monte Carlo simulation (AK-MCS), two milestone contributions in the field. In this paper, we first conduct a survey of the recent literature, showing that most of the proposed methods actually span from modifying one or more aspects of the two aforementioned methods. We then propose a generalized modular framework to build on-the-fly efficient active learning strategies by combining the following four ingredients or modules: surrogate model, reliability estimation algorithm, learning function and stopping criterion. Using this framework, we devise 39 strategies for the solution of 20 reliability benchmark problems. The results of this extensive benchmark (more than 12,000 reliability problems solved) are analyzed under various criteria leading to a synthesized set of recommendations for practitioners. These may be refined with a priori knowledge about the feature of the problem to solve, i.e. dimensionality and magnitude of the failure probability. This benchmark has eventually highlighted the importance of using surrogates in conjunction with sophisticated reliability estimation algorithms as a way to enhance the efficiency of the latter.},
  langid = {english},
  keywords = {Active learning,Benchmark,Gaussian process (Kriging),Polynomial chaos expansions,Structural reliability,Surrogate models},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Moustapha_et_al-Active_learning_for_structural_reliability_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\MTJW7JTS\\S0167473021000965.html}
}

@article{moustapha2022a,
  title = {Active Learning for Structural Reliability: {{Survey}}, General Framework and Benchmark},
  shorttitle = {Active Learning for Structural Reliability},
	author = {Moustapha, Maliki and Marelli, Stefano and Sudret, Bruno},
  year = {2022},
  journal = {Structural Safety},
  volume = {96},
  pages = {102174},
  urldate = {2023-11-16},
  abstract = {Active learning methods have recently surged in the literature due to their ability to solve complex structural reliability problems within an affordable computational cost. These methods are designed by adaptively building an inexpensive surrogate of the original limit-state function. Examples of such surrogates include Gaussian process models which have been adopted in many contributions, the most popular ones being the efficient global reliability analysis (EGRA) and the active Kriging Monte Carlo simulation (AK-MCS), two milestone contributions in the field. In this paper, we first conduct a survey of the recent literature, showing that most of the proposed methods actually span from modifying one or more aspects of the two aforementioned methods. We then propose a generalized modular framework to build on-the-fly efficient active learning strategies by combining the following four ingredients or modules: surrogate model, reliability estimation algorithm, learning function and stopping criterion. Using this framework, we devise 39 strategies for the solution of 20 reliability benchmark problems. The results of this extensive benchmark (more than 12,000 reliability problems solved) are analyzed under various criteria leading to a synthesized set of recommendations for practitioners. These may be refined with a priori knowledge about the feature of the problem to solve, i.e. dimensionality and magnitude of the failure probability. This benchmark has eventually highlighted the importance of using surrogates in conjunction with sophisticated reliability estimation algorithms as a way to enhance the efficiency of the latter.},
  keywords = {Active learning,Benchmark,Gaussian process (Kriging),Polynomial chaos expansions,Structural reliability,Surrogate models},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Reliability Analysis\Moustapha_et_al-Active_learning_for_structural_reliability_2022.pdf}
}

@article{moustapha2023,
  title = {Learning Non-Stationary and Discontinuous Functions Using Clustering, Classification and {{Gaussian}} Process Modelling},
	author = {Moustapha, Maliki and Sudret, Bruno},
  year = {2023},
  journal = {Computers \& Structures},
  volume = {281},
  pages = {107035},
  urldate = {2024-02-08},
  abstract = {Surrogate models have shown to be an extremely efficient aid in solving engineering problems that require repeated evaluations of an expensive computational model. They are built by sparsely evaluating the costly original model and have provided a way to solve otherwise intractable problems. A crucial aspect in surrogate modelling is the assumption of smoothness and regularity of the model to approximate. This assumption is however not always met in reality. For instance in civil or mechanical engineering, some models may present discontinuities or non-smoothness e.g., in case of instability patterns such as buckling or snap-through. Building a single surrogate model capable of accounting for these fundamentally different behaviours or discontinuities is not an easy task. In this paper, we propose a three-stage approach for the approximation of non-smooth functions which combines clustering, classification and regression. The idea is to split the space following the localized behaviors or regimes of the system and build local surrogates that are eventually assembled. A sequence of well-known machine learning techniques are used: Dirichlet process mixtures models (DPMM), support vector machines and Gaussian process modelling. The approach is tested and validated on two analytical functions and a finite element model of a tensile membrane structure.},
  keywords = {Dirichlet process mixture models,Discontinuities,Non-smooth functions,Surrogate modelling,Uncertainty quantification},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Moustapha_Sudret-Learning_non-stationary_and_discontinuous_functions_using_clustering,_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\CVYCLE3W\\S0045794923000652.html}
}

@article{mullins2016,
  title = {Separation of Aleatory and Epistemic Uncertainty in Probabilistic Model Validation},
	author = {Mullins, Joshua and Ling, You and Mahadevan, Sankaran and Sun, Lin and Strachan, Alejandro},
  year = {2016},
  journal = {Reliability Engineering \& System Safety},
  volume = {147},
  pages = {49--59},
  urldate = {2022-08-15},
  abstract = {This paper investigates model validation under a variety of different data scenarios and clarifies how different validation metrics may be appropriate for different scenarios. In the presence of multiple uncertainty sources, model validation metrics that compare the distributions of model prediction and observation are considered. Both ensemble validation and point-by-point approaches are discussed, and it is shown how applying the model reliability metric point-by-point enables the separation of contributions from aleatory and epistemic uncertainty sources. After individual validation assessments are made at different input conditions, it may be desirable to obtain an overall measure of model validity across the entire domain. This paper proposes an integration approach that assigns weights to the validation results according to the relevance of each validation test condition to the overall intended use of the model in prediction. Since uncertainty propagation for probabilistic validation is often unaffordable for complex computational models, surrogate models are often used; this paper proposes an approach to account for the additional uncertainty introduced in validation by the uncertain fit of the surrogate model. The proposed methods are demonstrated with a microelectromechanical system (MEMS) example.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\General\Mullins_et_al-Separation_of_aleatory_and_epistemic_uncertainty_in_probabilistic_model_2016.pdf}
}

@article{mullins2016a,
  title = {Optimal {{Test Selection}} for {{Prediction Uncertainty Reduction}}},
	author = {Mullins, Joshua and Mahadevan, Sankaran and Urbina, Angel},
  year = {2016},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {1},
  number = {4},
  pages = {041002},
  urldate = {2021-09-21},
  abstract = {Economic factors and experimental limitations often lead to sparse and/or imprecise data used for the calibration and validation of computational models. This paper addresses resource allocation for calibration and validation experiments, in order to maximize their effectiveness within given resource constraints. When observation data is used for model calibration, the quality of the inferred parameter descriptions is directly affected by the quality and quantity of the data. This paper characterizes parameter uncertainty within a probabilistic framework, which enables the uncertainty to be systematically reduced with additional data. The validation assessment is also uncertain in the presence of sparse and imprecise data; therefore, this paper proposes an approach for quantifying the resulting validation uncertainty. Since calibration and validation uncertainty affect the prediction of interest, the proposed framework explores the decision of cost vs. importance of data in terms of the impact on the prediction uncertainty. Often, calibration and validation tests may be performed for different input scenarios, and this paper shows how the calibration and validation results from different conditions may be integrated into the prediction. Then, a constrained discrete optimization formulation that selects the number of tests of each type (calibration or validation at given input conditions) is proposed.},
  langid = {english},
  keywords = {Efficient Model Validation,Model Calibration,Model Validation,Optimization,Uncertainty},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Validation\\Efficient Model Validation\\Mullins_et_al-Optimal_Test_Selection_for_Prediction_Uncertainty_Reduction_2016.pdf;C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Validation\\Efficient Model Validation\\Mullins_et_al-Optimal_Test_Selection_for_Prediction_Uncertainty_Reduction_22.pdf}
}

@book{murphy2012,
  title = {Machine Learning: A Probabilistic Perspective},
  shorttitle = {Machine Learning},
	author = {Murphy, Kevin P.},
  year = {2012},
  series = {Adaptive Computation and Machine Learning Series},
  publisher = {MIT Press},
  address = {Cambridge, MA},
  langid = {english},
  lccn = {Q325.5 .M87 2012},
  keywords = {Basics,Classification,Gaussian processes,Machine learning,Probabilistic Machine Learning,Probabilities,Regression},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Murphy-Machine_learning_2012.pdf}
}

@article{nagel2016,
  title = {A Unified Framework for Multilevel Uncertainty Quantification in {{Bayesian}} Inverse Problems},
	author = {Nagel, Joseph B. and Sudret, Bruno},
  year = {2016},
  journal = {Probabilistic Engineering Mechanics},
  volume = {43},
  pages = {68--84},
  urldate = {2023-05-13},
  abstract = {In this paper a unified probabilistic framework for solving inverse problems in the presence of epistemic and aleatory uncertainty is presented. The aim is to establish a flexible theory that facilitates Bayesian data analysis in experimental scenarios as they are commonly met in engineering practice. Problems are addressed where learning about unobservable inputs of a forward model, e.g. reducing the epistemic uncertainty of fixed yet unknown parameters and/or quantifying the aleatory uncertainty of variable inputs, is based on processing response measurements. Approaches to Bayesian inversion, hierarchical modeling and uncertainty quantification are combined into a generic framework that eventually allows to interpret and accomplish this task as multilevel model calibration. A joint problem formulation, where quantities that are not of particular interest are marginalized out from a joint posterior distribution, or an intrinsically marginal formulation, which is based on an integrated likelihood function, can be chosen according to the inferential objective and computational convenience. Fully Bayesian probabilistic inversion, i.e. the inference the variability of unobservable model inputs across a number of experiments, is derived as a special case of multilevel inversion. Borrowing strength, i.e. the optimal estimation of experiment-specific unknown forward model inputs, is introduced as a means for combining information in inverse problems. Two related statistical models for situations involving finite or zero model/measurement error are devised. Multilevel-specific obstacles to Bayesian posterior computation via Markov chain Monte Carlo are discussed. The inferential machinery of Bayesian multilevel model calibration and its underlying flow of information are studied on the basis of a system from the domain of civil engineering. A population of identically manufactured structural elements serves as an exemplary system for examining different experimental settings from the standpoint of uncertainty quantification and reduction. In a series of tests the material variability throughout the ensemble of specimens, the entirety of specimen-specific material properties and the measurement error level are inferred under various uncertainties in the problem setup.},
  langid = {english},
  keywords = {Bayesian inference,Borrowing strength,Hierarchical modeling,Inverse problems,Markov chain Monte Carlo,Probabilistic inversion,Uncertainty quantification},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\Nagel_Sudret-A_unified_framework_for_multilevel_uncertainty_quantification_in_Bayesian_2016.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\NI9NTE7G\\S0266892015300266.html}
}

@standard{NASA7009A,
  title = {Nasa-Std-7009a - Standard for Models and Simulations},
  year = {2016},
  publisher = {{National Aeronautics and Space Administration}}
}

@book{neal1996,
  title = {Bayesian {{Learning}} for {{Neural Networks}}.},
	author = {Neal, Radford M.},
  year = {1996},
  series = {Lecture {{Notes}} in {{Statistics}}},
  publisher = {Springer New York},
  address = {New York},
  urldate = {2022-08-05},
  langid = {english}
}

@incollection{neal2011,
  title = {{{MCMC}} Using {{Hamiltonian}} Dynamics},
  booktitle = {Handbook of {{Markov Chain Monte Carlo}}},
	author = {Neal, Radford M.},
  year = {2011},
  volume = {2},
  eprint = {1206.1901},
  urldate = {2022-01-04},
  abstract = {Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though originating in physics, Hamiltonian dynamics can be applied to most problems with continuous state spaces by simply introducing fictitious "momentum" variables. A key to its usefulness is that Hamiltonian dynamics preserves volume, and its trajectories can thus be used to define complex mappings without the need to account for a hard-to-compute Jacobian factor - a property that can be exactly maintained even when the dynamics is approximated by discretizing time. In this review, I discuss theoretical and practical aspects of Hamiltonian Monte Carlo, and present some of its variations, including using windows of states for deciding on acceptance or rejection, computing trajectories using fast approximations, tempering during the course of a trajectory to handle isolated modes, and short-cut methods that prevent useless trajectories from taking much computation time.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Physics - Computational Physics,Statistics - Computation},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Bayesian Inference\Neal-MCMC_using_Hamiltonian_dynamics_2011.pdf}
}

@inproceedings{neiswanger2021,
  title = {Bayesian {{Algorithm Execution}}: {{Estimating Computable Properties}} of {{Black-Box Functions}} Using {{Mutual Information}}},
  booktitle = {Proceedings of the 38th {{International Conference}} on {{Machine Learning}}},
	author = {Neiswanger, Willie and Wang, Ke Alexander and Ermon, Stefano},
  year = {2021},
  volume = {139},
  pages = {8005--8015},
  publisher = {PMLR},
  abstract = {In many real world problems, we want to infer some property of an expensive black-box function f, given a budget of T function evaluations. One example is budget constrained global optimization of f, for which Bayesian optimization is a popular method. Other properties of interest include local optima, level sets, integrals, or graph-structured information induced by f. Often, we can find an algorithm A to compute the desired property, but it may require far more than T queries to execute. Given such an A, and a prior distribution over f, we refer to the problem of inferring the output of A using T evaluations as Bayesian Algorithm Execution (BAX). To tackle this problem, we present a procedure, InfoBAX, that sequentially chooses queries that maximize mutual information with respect to the algorithm's output. Applying this to Dijkstra's algorithm, for instance, we infer shortest paths in synthetic and real-world graphs with black-box edge costs. Using evolution strategies, we yield variants of Bayesian optimization that target local, rather than global, optima. On these problems, InfoBAX uses up to 500 times fewer queries to f than required by the original algorithm. Our method is closely connected to other Bayesian optimal experimental design procedures such as entropy search methods and optimal sensor placement using Gaussian processes.}
}

@misc{nemani2023,
  title = {Uncertainty {{Quantification}} in {{Machine Learning}} for {{Engineering Design}} and {{Health Prognostics}}: {{A Tutorial}}},
  shorttitle = {Uncertainty {{Quantification}} in {{Machine Learning}} for {{Engineering Design}} and {{Health Prognostics}}},
	author = {Nemani, Venkat and Biggio, Luca and Huan, Xun and Hu, Zhen and Fink, Olga and others},
  year = {2023},
  number = {arXiv:2305.04933},
  eprint = {2305.04933},
  primaryclass = {cs},
  publisher = {arXiv},
  urldate = {2023-09-22},
  abstract = {On top of machine learning models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and reliability improvement of ML models empowered by UQ has the potential to significantly facilitate the broad adoption of ML solutions in high-stakes decision settings, such as healthcare, manufacturing, and aviation, to name a few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods for ML models with a particular focus on neural networks and the applications of these UQ methods in tackling engineering design as well as prognostics and health management problems. Toward this goal, we start with a comprehensive classification of uncertainty types, sources, and causes pertaining to UQ of ML models. Next, we provide a tutorial-style description of several state-of-the-art UQ methods: Gaussian process regression, Bayesian neural network, neural network ensemble, and deterministic UQ methods focusing on spectral-normalized neural Gaussian process. Established upon the mathematical formulations, we subsequently examine the soundness of these UQ methods quantitatively and qualitatively (by a toy regression example) to examine their strengths and shortcomings from different dimensions. Then, we review quantitative metrics commonly used to assess the quality of predictive uncertainty in classification and regression problems. Afterward, we discuss the increasingly important role of UQ of ML models in solving challenging problems in engineering design and health prognostics. Two case studies with source codes available on GitHub are used to demonstrate these UQ methods and compare their performance in the life prediction of lithium-ion batteries at the early stage and the remaining useful life prediction of turbofan engines.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Uncertainty Quantification\\Nemani_et_al-Uncertainty_Quantification_in_Machine_Learning_for_Engineering_Design_and_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\YRPP6QE7\\2305.html}
}

@article{ng2014,
  title = {Multifidelity Approaches for Optimization under Uncertainty},
	author = {Ng, Leo W. T. and Willcox, Karen E.},
  year = {2014},
  journal = {International Journal for Numerical Methods in Engineering},
  volume = {100},
  number = {10},
  pages = {746--772},
  urldate = {2023-02-04},
  abstract = {SUMMARYIt is important to design robust and reliable systems by accounting for uncertainty and variability in the design process. However, performing optimization in this setting can be computationally expensive, requiring many evaluations of the numerical model to compute statistics of the system performance at every optimization iteration. This paper proposes a multifidelity approach to optimization under uncertainty that makes use of inexpensive, low-fidelity models to provide approximate information about the expensive, high-fidelity model. The multifidelity estimator is developed based on the control variate method to reduce the computational cost of achieving a specified mean square error in the statistic estimate. The method optimally allocates the computational load between the two models based on their relative evaluation cost and the strength of the correlation between them. This paper also develops an information reuse estimator that exploits the autocorrelation structure of the high-fidelity model in the design space to reduce the cost of repeatedly estimating statistics during the course of optimization. Finally, a combined estimator incorporates the features of both the multifidelity estimator and the information reuse estimator. The methods demonstrate 90\% computational savings in an acoustic horn robust optimization example and practical design turnaround time in a robust wing optimization problem. Copyright {\copyright} 2014 John Wiley \& Sons, Ltd.},
  langid = {english},
  keywords = {design under uncertainty,model reduction,multifidelity,optimization,probabilistic methods,stochastic problems},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Ng_Willcox-Multifidelity_approaches_for_optimization_under_uncertainty_2014.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\JU2C5W23\\nme.html}
}

@misc{ober2021,
  title = {The {{Promises}} and {{Pitfalls}} of {{Deep Kernel Learning}}},
	author = {Ober, Sebastian W. and Rasmussen, Carl E. and {van der Wilk}, Mark},
  year = {2021},
  number = {arXiv:2102.12108},
  eprint = {2102.12108},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {Deep kernel learning (DKL) and related techniques aim to combine the representational power of neural networks with the reliable uncertainty estimates of Gaussian processes. One crucial aspect of these models is an expectation that, because they are treated as Gaussian process models optimized using the marginal likelihood, they are protected from overfitting. However, we identify situations where this is not the case. We explore this behavior, explain its origins and consider how it applies to real datasets. Through careful experimentation on the UCI, CIFAR-10, and the UTKFace datasets, we find that the overfitting from overparameterized maximum marginal likelihood, in which the model is "somewhat Bayesian", can in certain scenarios be worse than that from not being Bayesian at all. We explain how and when DKL can still be successful by investigating optimization dynamics. We also find that failures of DKL can be rectified by a fully Bayesian treatment, which leads to the desired performance improvements over standard neural networks and Gaussian processes.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Ober_et_al-The_Promises_and_Pitfalls_of_Deep_Kernel_Learning_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\E9PQSM3H\\2102.html}
}

@article{oberkampf2006,
  title = {Measures of Agreement between Computation and Experiment: {{Validation}} Metrics},
	author = {Oberkampf, William L. and Barone, Matthew F.},
  year = {2006},
  journal = {Journal of Computational Physics},
  volume = {217},
  number = {1},
  pages = {5--36},
}

@book{oberkampf2010,
  title = {Verification and {{Validation}} in {{Scientific Computing}}},
	author = {Oberkampf, William L. and Roy, Christopher J.},
  year = {2010},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  urldate = {2021-09-07},
  langid = {english},
  keywords = {Area Metric,Basics,Examples,Frequentist,Model Validation,U-Pooling,Uncertainty,Validation Metric},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\General\Oberkampf_Roy-Verification_and_Validation_in_Scientific_Computing_2010.pdf}
}

@article{obermayr2021,
  title = {A Novel Online 4-Point Rainflow Counting Algorithm for Power Electronics},
	author = {Obermayr, Martin and Riess, Christian and Wilde, J{\"u}rgen},
  year = {2021},
  journal = {Microelectronics Reliability},
  volume = {120},
  pages = {114112},
  urldate = {2022-03-09},
  langid = {english}
}

@article{OpenML2013,
  title = {{{OpenML}}: Networked Science in Machine Learning},
	author = {Vanschoren, Joaquin and {van Rijn}, Jan N. and Bischl, Bernd and Torgo, Luis},
  year = {2013},
  journal = {SIGKDD Explorations},
  volume = {15},
  number = {2},
  pages = {49--60},
  publisher = {ACM},
}

@inproceedings{osborne2012,
  title = {Active {{Learning}} of {{Model Evidence Using Bayesian Quadrature}}},
  booktitle = {Advances in {{Neural Information Processing Systems}}},
	author = {Osborne, Michael and Garnett, Roman and Ghahramani, Zoubin and Duvenaud, David K and Roberts, Stephen J and others},
  year = {2012},
  volume = {25},
  publisher = {Curran Associates, Inc.},
  urldate = {2023-12-12},
  abstract = {Numerical integration is an key component of many problems in scientific computing, statistical modelling, and machine learning. Bayesian Quadrature is a model-based method for numerical integration which, relative to standard Monte Carlo methods, offers increased sample efficiency and a more robust estimate of the uncertainty in the estimated integral. We propose a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model. Our approach approximately marginalises the quadrature model's hyperparameters in closed form, and introduces an active learning scheme to optimally select function evaluations, as opposed to using Monte Carlo samples. We demonstrate our method on both a number of synthetic benchmarks and a real scientific problem from astronomy.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Osborne_et_al-Active_Learning_of_Model_Evidence_Using_Bayesian_Quadrature_2012.pdf}
}

@article{osti_1420250,
  title = {A Survey of Methods for Integration of Uncertainty and Model Form Error in Prediction.},
	author = {Mullins, Joshua Grady and Schroeder, Benjamin B and Hills, Richard G. and Crespo, Luis G.},
  year = {2016},
  address = {United States},
  annotation = {Abstract Note: Abstract not provided.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Mullins_et_al-A_survey_of_methods_for_integration_of_uncertainty_and_model_form_error_in_2016.pdf}
}

@book{owen2013,
  title = {Monte {{Carlo}} Theory, Methods and Examples},
	author = {Owen, Art B.},
  year = {2013}
}

@article{paez2008,
  title = {Structural {{Dynamics Challenge Problem}}: {{Summary}}},
  shorttitle = {Structural {{Dynamics Challenge Problem}}},
	author = {Paez, Thomas L. and {Red-Horse}, John},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2660--2665},
  urldate = {2021-09-07},
  abstract = {The six papers in this special issue that develop solutions to the Structural Dynamics Challenge Problem are summarized herein. The goal is to emphasize different tools and approaches applied to various parts of the structural dynamics problem. Specifically the following issues are considered: (1) Development of a mathematical framework for uncertainty quantification of a substructure. (2) Calibration of a mathematical model for the substructure. (3) Validation of the substructure mathematical model. (4) Use of the mathematical model of the substructure, in conjunction with another structure, to make a prediction of the probability that a regulatory limit is surpassed, and discussion of the uncertainty of the prediction. Different methodologies are presented and specific results vary, however, conclusions regarding satisfaction of the regulatory requirement match.},
  langid = {english},
  keywords = {Model Validation,Sandia Workshop},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\ValidationWS Sandia Lab\Paez_Red-Horse-Structural_Dynamics_Challenge_Problem_2008.pdf}
}

@inproceedings{papadopoulos2002,
  title = {Inductive {{Confidence Machines}} for {{Regression}}},
  booktitle = {Machine {{Learning}}: {{ECML}} 2002},
	author = {Papadopoulos, Harris and Proedrou, Kostas and Vovk, Volodya and Gammerman, Alex},
  year = {2002},
  pages = {345--356},
  publisher = {Springer},
  address = {Berlin},
  abstract = {The existing methods of predicting with confidence give good accuracy and confidence values, but quite often are computationally inefficient. Some partial solutions have been suggested in the past. Both the original method and these solutions were based on transductive inference. In this paper we make a radical step of replacing transductive inference with inductive inference and define what we call the Inductive Confidence Machine (ICM); our main concern in this paper is the use of ICM in regression problems. The algorithm proposed in this paper is based on the Ridge Regression procedure (which is usually used for outputting bare predictions) and is much faster than the existing transductive techniques. The inductive approach described in this paper may be the only option available when dealing with large data sets.},
  langid = {english},
  keywords = {Inductive Inference,Kolmogorov Complexity,Ridge Regression,Tolerance Region,True Label},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Conformal Prediction\Papadopoulos_et_al-Inductive_Confidence_Machines_for_Regression_2002.pdf}
}

@misc{papadopoulos2023,
  title = {Guaranteed {{Coverage Prediction Intervals}} with {{Gaussian Process Regression}}},
	author = {Papadopoulos, Harris},
  year = {2023},
  number = {arXiv:2310.15641},
  eprint = {2310.15641},
  primaryclass = {cs},
  publisher = {arXiv},
  urldate = {2024-03-05},
  abstract = {Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that the model is well-specified, an assumption that is violated in most practical applications, since the required knowledge is rarely available. As a result, the produced uncertainty estimates can become very misleading; for example the prediction intervals (PIs) produced for the 95{\textbackslash}\% confidence level may cover much less than 95{\textbackslash}\% of the true labels. To address this issue, this paper introduces an extension of GPR based on a Machine Learning framework called, Conformal Prediction (CP). This extension guarantees the production of PIs with the required coverage even when the model is completely misspecified. The proposed approach combines the advantages of GPR with the valid coverage guarantee of CP, while the performed experimental results demonstrate its superiority over existing methods.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Conformal Prediction\\Papadopoulos-Guaranteed_Coverage_Prediction_Intervals_with_Gaussian_Process_Regression_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\9G87VN85\\2310.html}
}

@article{papadrakakis1996,
  title = {Structural Reliability Analyis of Elastic-Plastic Structures Using Neural Networks and {{Monte Carlo}} Simulation},
	author = {Papadrakakis, Manolis and Papadopoulos, Vissarion and Lagaros, Nikos D.},
  year = {1996},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {136},
  pages = {145--163}
}

@article{papadrakakis2001,
  title = {Large Scale Structural Optimization: {{Computational}} Methods and Optimization Algorithms},
  shorttitle = {Large Scale Structural Optimization},
	author = {Papadrakakis, M. and Lagaros, N. D. and Tsompanakis, Y. and Plevris, V.},
  year = {2001},
  journal = {Archives of Computational Methods in Engineering},
  volume = {8},
  number = {3},
  pages = {239--301},
  urldate = {2022-01-20},
  langid = {english}
}

@article{paquette-rufiange2023,
  title = {Optimal Design of Validation Experiments for the Prediction of Quantities of Interest},
	author = {{Paquette-Rufiange}, Antonin and Prudhomme, Serge and Laforest, Marc},
  year = {2023},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {414},
  pages = {116182},
  urldate = {2023-08-24},
  abstract = {Numerical predictions of quantities of interest measured within physical systems rely on the use of mathematical models that should be validated, or at best, not invalidated. Model validation usually involves the comparison of experimental data (outputs from the system of interest) and model predictions, both obtained at a specific validation scenario. The design of this validation experiment should be directly relevant to the objective of the model, that of predicting a quantity of interest at a prediction scenario. In this paper, we address two specific issues arising when designing validation experiments. The first issue consists in determining an appropriate validation scenario in cases where the prediction scenario cannot be carried out in a controlled environment. The second issue concerns the selection of observations when the quantity of interest cannot be readily observed. The proposed methodology involves the computation of influence matrices that characterize the response surface of given model functionals. Minimization of the distance between influence matrices allows one to select a validation experiment most representative of the prediction scenario. We illustrate our approach on two numerical examples. The first example considers the validation of a simple model based on an ordinary differential equation governing an object in free fall to put in evidence the importance of the choice of the validation experiment. The second numerical experiment focuses on the transport of a pollutant and demonstrates the impact that the choice of the quantity of interest has on the validation experiment to be performed.},
  keywords = {Optimal design of experiments,Quantity of interest,Sensitivity analysis,Uncertainty quantification,Validation},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Validation\\Efficient Model Validation\\Paquette-Rufiange_et_al-Optimal_design_of_validation_experiments_for_the_prediction_of_quantities_of_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\SRUYYI5G\\S0045782523003067.html}
}

@article{paszke2019,
  title = {{{PyTorch}}: {{An Imperative Style}}, {{High-Performance Deep Learning Library}}},
  shorttitle = {{{PyTorch}}},
	author = {Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and others},
  year = {2019},
  journal = {arXiv:1912.01703},
  eprint = {1912.01703},
  urldate = {2022-02-14},
  abstract = {Deep learning frameworks have often focused on either usability or speed, but not both. PyTorch is a machine learning library that shows that these two goals are in fact compatible: it provides an imperative and Pythonic programming style that supports code as a model, makes debugging easy and is consistent with other popular scientific computing libraries, while remaining efficient and supporting hardware accelerators such as GPUs. In this paper, we detail the principles that drove the implementation of PyTorch and how they are reflected in its architecture. We emphasize that every aspect of PyTorch is a regular Python program under the full control of its user. We also explain how the careful and pragmatic implementation of the key components of its runtime enables them to work together to achieve compelling performance. We demonstrate the efficiency of individual subsystems, as well as the overall speed of PyTorch on several common benchmarks.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Computer Science - Mathematical Software,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Software_Packages\\Paszke_et_al-PyTorch_2019.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\MIJ4KEP8\\1912.html}
}

@article{pedregosa2011,
  title = {Scikit-Learn: {{Machine Learning}} in {{Python}}},
	author = {Pedregosa, Fabian and Varoquaux, Gael and Gramfort, Alexandre and Michel, Vincent and Thirion, Bertrand and others},
  year = {2011},
  journal = {Journal of Machine Learning Research},
  volume = {12},
  pages = {2825--2830}
}

@article{pernot2017,
  title = {A Critical Review of Statistical Calibration/Prediction Models Handling Data Inconsistency and Model Inadequacy},
	author = {Pernot, Pascal and Cailliez, Fabien},
  year = {2017},
  journal = {AIChE Journal},
  volume = {63},
  number = {10},
  eprint = {1611.04376},
  primaryclass = {physics},
  pages = {4642--4665},
  urldate = {2023-05-10},
  abstract = {Inference of physical parameters from reference data is a well studied problem with many intricacies (inconsistent sets of data due to experimental systematic errors; approximate physical models...). The complexity is further increased when the inferred parameters are used to make predictions -- virtual measurements -- because parameters uncertainty has to be estimated in addition to parameters best value. The literature is rich in statistical models for the calibration/prediction problem, each having benefits and limitations.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Physics - Chemical Physics,Physics - Data Analysis Statistics and Probability},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\SF7398LR\Pernot and Cailliez - 2017 - A critical review of statistical calibrationpredi.pdf}
}

@article{pernot2017a,
  title = {A Critical Review of Statistical Calibration/Prediction Models Handling Data Inconsistency and Model Inadequacy},
	author = {Pernot, Pascal and Cailliez, Fabien},
  year = {2017},
  journal = {AIChE Journal},
  volume = {63},
  number = {10},
  pages = {4642--4665},
  urldate = {2023-09-22},
  abstract = {Inference of physical parameters from reference data is a well-studied problem with many intricacies (inconsistent sets of data due to experimental systematic errors; approximate physical models{\dots}). The complexity is further increased when the inferred parameters are used to make predictions---virtual measurements---because parameter uncertainty has to be estimated in addition to parameters best value. The literature is rich in statistical models for the calibration/prediction problem, each having benefits and limitations. We review and evaluate standard and state-of-the-art statistical models in a common Bayesian framework, and test them on synthetic and real datasets of temperature-dependent viscosity for the calibration of the Lennard-Jones parameters of a Chapman-Enskog model. {\copyright} 2017 American Institute of Chemical Engineers AIChE J, 63: 4642--4665, 2017},
  copyright = {{\copyright} 2017 American Institute of Chemical Engineers},
  langid = {english},
  keywords = {data reconciliation,diffusion,mathematical modeling,statistical analysis},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\DBC\\KOH\\Pernot_Cailliez-A_critical_review_of_statistical_calibration-prediction_models_handling_data_2017.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\UUGGCK8N\\aic.html}
}

@misc{petersen2012,
  title = {The {{Matrix Cookbook}}},
	author = {Petersen, Kaare Brandt and Pedersen, Michael Syskind},
  year = {2012},
  langid = {english},
  keywords = {Gaussian Distribution,Linear Algebra,Mathematics,Matrix,Statistics,Vectors},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Petersen_Pedersen-The_Matrix_Cookbook_2012.pdf}
}

@inproceedings{pfeiler2012,
  title = {A {{Bayesian Mixture Coffin-Manson Approach}} to {{Predict Semiconductor Lifetime}}},
	author = {Pfeiler, Olivia and Pilz, J{\"u}rgen and Glavanovics, Michael and Plankensteiner, Kathrin},
  year = {2012},
  abstract = {Based on physical failure inspection, known physical relationships, correlation analysis and posterior predictive distributions, a valid model for semiconductor lifetime is developed. It is shown that the data follow a mixture of two normal distributions and that the mixture weights depend on the destruction level. The mean lifetime of each component is modeled with an extended Coffin-Manson model. As priors, a combination of normal and hierarchical inverse gamma distributions is used. Since the given data show censoring, this is not a conjugate setting and the posterior distributions are simulated with MCMC methods. Model verifi{\dbend}cation, based on the posterior predictive distribution, con{\dbend}firms good prediction quality for interpolations and shows potential for improving extrapolations.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Lifetime Coffin Manson\Pfeiler_et_al-A_Bayesian_Mixture_Coffin-Manson_Approach_to_Predict_Semiconductor_Lifetime_2012.pdf}
}

@article{pilosov2023,
  title = {Parameter Estimation with Maximal Updated Densities},
	author = {Pilosov, Michael and {del-Castillo-Negrete}, Carlos and Yen, Tian Yu and Butler, Troy and Dawson, Clint},
  year = {2023},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {407},
  pages = {115906},
  urldate = {2023-07-28},
  abstract = {A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e., parameters). The subsequent inferential target is a distribution on parameters. Another type of inverse problem is to quantify uncertainties in estimates of ``true'' parameter values under the assumption that such uncertainties should be reduced as more data are incorporated into the problem, i.e., the uncertainty is considered epistemic. A major contribution of this work is the formulation and solution of such a parameter identification problem (PIP) within the measure-theoretic framework developed for the SIP. The approach is novel in that it utilizes a solution to a stochastic forward problem (SFP) to update an initial density only in the parameter directions informed by the model output data. In other words, this method performs ``selective regularization'' only in the parameter directions not informed by data. The solution is defined by a maximal updated density (MUD) point where the updated density defines the measure-theoretic solution to the PIP. Another significant contribution of this work is the full theory of existence and uniqueness of MUD points for linear maps with Gaussian distributions. Data-constructed Quantity of Interest (QoI) maps are also presented and analyzed for solving the PIP within this measure-theoretic framework as a means of reducing uncertainties in the MUD estimate. We conclude with a demonstration of the general applicability of the method on two problems involving either spatial or temporal data for estimating uncertain model parameters. The first problem utilizes spatial data from a stationary partial differential equation to produce a MUD estimate of an uncertain boundary condition. The second problem utilizes temporal data obtained from the state-of-the-art ADvanced CIRCulation (ADCIRC) model to obtain a MUD estimate of uncertain wind drag coefficients for a simulated extreme weather event near the Shinnecock Inlet located in the Outer Barrier of Long Island, NY, USA.},
  langid = {english},
  keywords = {Inverse problems,Parameter estimation,Pullback measure,Push-forward measure,Uncertainty quantification},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\PushForward Inference\\Pilosov_et_al-Parameter_estimation_with_maximal_updated_densities_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\MCFBCJTK\\S0045782523000294.html}
}

@article{plumlee2017,
  title = {Bayesian {{Calibration}} of {{Inexact Computer Models}}},
	author = {Plumlee, Matthew},
  year = {2017},
  journal = {Journal of the American Statistical Association},
  volume = {112},
  number = {519},
  pages = {1274--1285},
  publisher = {Taylor \& Francis},
  urldate = {2023-05-10},
  abstract = {Bayesian calibration is used to study computer models in the presence of both a calibration parameter and model bias. The parameter in the predominant methodology is left undefined. This results in an issue, where the posterior of the parameter is suboptimally broad. There has been no generally accepted alternatives to date. This article proposes using Bayesian calibration, where the prior distribution on the bias is orthogonal to the gradient of the computer model. Problems associated with Bayesian calibration are shown to be mitigated through analytic results in addition to examples. Supplementary materials for this article are available online.},
  keywords = {Calibration,Computer experiments,Deterministic models,Gaussian processes,Identifiability,Kriging,Model inadequacy,Orthogonal processes,Uncertainty quantification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\DBC\KOH\Plumlee-Bayesian_Calibration_of_Inexact_Computer_Models_2017.pdf}
}

@article{plumlee2019,
  title = {Computer Model Calibration with Confidence and Consistency},
	author = {Plumlee, Matthew},
  year = {2019},
  journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume = {81},
  number = {3},
  pages = {519--545},
  urldate = {2023-02-04},
  abstract = {The paper proposes and examines a calibration method for inexact models. The method produces a confidence set on the parameters that includes the best parameter with a desired probability under any sample size. Additionally, this confidence set is shown to be consistent in that it excludes suboptimal parameters in large sample environments. The method works and the results hold with few assumptions; the ideas are maintained even with discrete input spaces or parameter spaces. Computation of the confidence sets and approximate confidence sets is discussed. The performance is illustrated in a simulation example as well as two real data examples.},
  langid = {english},
  keywords = {Frequentist,Inverse problem,Model discrepancy,Model inadequacy,Model misspecification,Non-linear regression,Uncertainty quantification},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\Plumlee-Computer_model_calibration_with_confidence_and_consistency_2019.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\WBXLK46A\\rssb.html}
}

@book{rasmussen2006,
  title = {Gaussian Processes for Machine Learning},
	author = {Rasmussen, Carl Edward and Williams, Christopher K. I.},
  year = {2006},
  series = {Adaptive Computation and Machine Learning},
  publisher = {MIT Press},
  address = {Cambridge},
  langid = {english},
  keywords = {Basics,Classification,Data processing,Gaussian processes,Machine learning,Mathematical models,Probabilistic Machine Learning,Regression},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Rasmussen_Williams-Gaussian_processes_for_machine_learning_2006.pdf}
}

@phdthesis{rebba2005,
  title = {{{MODEL VALIDATION AND DESIGN UNDER UNCERTAINTY}}},
	author = {Rebba, Ramesh},
  year = {2005},
  langid = {english},
  keywords = {Dissertation,Model Validation,Uncertainty},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\General\Rebba-MODEL_VALIDATION_AND_DESIGN_UNDER_UNCERTAINTY_2005.pdf}
}

@article{rebba2008,
  title = {Computational Methods for Model Reliability Assessment},
	author = {Rebba, Ramesh and Mahadevan, Sankaran},
  year = {2008},
  journal = {Reliability Engineering \& System Safety},
  volume = {93},
  number = {8},
  pages = {1197--1207},
  urldate = {2023-01-30},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Rebba_Mahadevan-Computational_methods_for_model_reliability_assessment_2008.pdf}
}

@article{red-horse2008,
  title = {Sandia {{National Laboratories Validation Workshop}}: {{Structural}} Dynamics Application},
  shorttitle = {Sandia {{National Laboratories Validation Workshop}}},
	author = {{Red-Horse}, J.R. and Paez, T.L.},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2578--2584},
  urldate = {2021-09-07},
  abstract = {This article specifies a virtual structural dynamic subsystem and some systems, as well as mathematical models that approximately simulate them. The purpose is to define a setting for model validations conceived by participants in the Sandia National Laboratories Validation Workshop. Some broad guidelines for the model validations are set, as well as a regulatory requirement to be satisfied by the target system. Participants are directed to present techniques for subsystem model validation, to analytically predict whether or not the regulatory requirement will be met, and to estimate the likelihood of accuracy of the prediction.},
  langid = {english},
  keywords = {Examples,Model Validation,Sandia Workshop,Validation Problem},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\ValidationWS Sandia Lab\Red-Horse_Paez-Sandia_National_Laboratories_Validation_Workshop_2008.pdf}
}

@inproceedings{reeb2023,
  title = {Validation of Composite Systems by Discrepancy Propagation},
  booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence},
	author = {Reeb, David and Patel, Kanil and Barsim, Karim Said and Schiegg, Martin and Gerwinn, Sebastian},
  year = {2023},
  volume = {216},
  pages = {1730--1740},
  publisher = {PMLR},
  abstract = {Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation offers a promising and less expensive alternative, but requires an assessment of the simulation accuracy and therefore end-to-end measurements. Additionally, covariate shifts between simulations and actual usage can cause difficulties for estimating the reliability of such systems. In this work, we present a validation method that propagates bounds on distributional discrepancy measures through a composite system, thereby allowing us to derive an upper bound on the failure probability of the real system from potentially inaccurate simulations. Each propagation step entails an optimization problem, where -- for measures such as maximum mean discrepancy (MMD) -- we develop tight convex relaxations based on semidefinite programs. We demonstrate that our propagation method yields valid and useful bounds for composite systems exhibiting a variety of realistic effects. In particular, we show that the proposed method can successfully account for data shifts within the experimental design as well as model inaccuracies within the simulation.},
  file = {C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\YE27JK3S\\reeb23a-supp.pdf;C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Reliability Analysis\\Reeb_et_al-Validation_of_composite_systems_by_discrepancy_propagation_2023.pdf}
}

@article{riedmaier2020,
  title = {Unified {{Framework}} and {{Survey}} for {{Model Verification}}, {{Validation}} and {{Uncertainty Quantification}}},
	author = {Riedmaier, Stefan and Danquah, Benedikt and Schick, Bernhard and Diermeyer, Frank},
  year = {2020},
  journal = {Archives of Computational Methods in Engineering},
  volume = {28},
  number = {4},
  pages = {2655--2688},
  urldate = {2021-09-10},
  abstract = {Simulation is becoming increasingly important in the development, testing and approval process in many areas of engineering, ranging from finite element models to highly complex cyber-physical systems such as autonomous cars. Simulation must be accompanied by model verification, validation and uncertainty quantification (VV\&UQ) activities to assess the inherent errors and uncertainties of each simulation model. However, the VV\&UQ methods differ greatly between the application areas. In general, a major challenge is the aggregation of uncertainties from calibration and validation experiments to the actual model predictions under new, untested conditions. This is especially relevant due to high extrapolation uncertainties, if the experimental conditions differ strongly from the prediction conditions, or if the output quantities required for prediction cannot be measured during the experiments. In this paper, both the heterogeneous VV\&UQ landscape and the challenge of aggregation will be addressed with a novel modular and unified framework to enable credible decision making based on simulation models. This paper contains a comprehensive survey of over 200 literature sources from many application areas and embeds them into the unified framework. In addition, this paper analyzes and compares the VV\&UQ methods and the application areas in order to identify strengths and weaknesses and to derive further research directions. The framework thus combines a variety of VV\&UQ methods, so that different engineering areas can benefit from new methods and combinations. Finally, this paper presents a procedure to select a suitable method from the framework for the desired application.},
  langid = {english},
  keywords = {Framework,Model Validation,Survey,Uncertainty Quantification,Validation Metric,Verification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Frameworks\Riedmaier_et_al-Unified_Framework_and_Survey_for_Model_Verification,_Validation_and_Uncertainty_2020.pdf}
}

@phdthesis{riedmaier2022,
  title = {Model Validation and Uncertainty Aggregation for Safety Assessment of Automated Vehicles},
	author = {Riedmaier, Stefan},
  year = {2022},
  abstract = {This dissertation presents a methodology for validation of simulation models to ensure virtual safeguarding of automated vehicles. The methodology quantifies model uncertainties compared to real experiments and predicts them by a data-driven approach to the virtual safeguarding scenarios. This provides statistical guarantees for reliable decision making. The methodology is first introduced generically and then configured, implemented, and evaluated specifically for safeguarding.},
  langid = {english},
  school = {Technische Universit{\"a}t M{\"u}nchen},
  keywords = {automated driving,data science,Model validation,safety assessment,statistics,uncertainty quantification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Riedmaier-Model_validation_and_uncertainty_aggregation_for_safety_assessment_of_automated_2022.pdf}
}

@article{riis2022,
  title = {Bayesian {{Active Learning}} with {{Fully Bayesian Gaussian Processes}}},
	author = {Riis, Christoffer and Antunes, Francisco and H{\"u}ttel, Frederik and Lima Azevedo, Carlos and Pereira, Francisco},
  year = {2022},
  journal = {Advances in Neural Information Processing Systems},
  volume = {35},
  pages = {12141--12153},
  urldate = {2023-12-13},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Active Learning\Riis_et_al-Bayesian_Active_Learning_with_Fully_Bayesian_Gaussian_Processes_2022.pdf}
}

@article{ritter2021,
  title = {{{TyXe}}: {{Pyro-based Bayesian}} Neural Nets for {{Pytorch}}},
  shorttitle = {{{TyXe}}},
	author = {Ritter, Hippolyt and Karaletsos, Theofanis},
  year = {2021},
  journal = {arXiv:2110.00276},
  eprint = {2110.00276},
  urldate = {2022-02-14},
  abstract = {We introduce TyXe, a Bayesian neural network library built on top of Pytorch and Pyro. Our leading design principle is to cleanly separate architecture, prior, inference and likelihood specification, allowing for a flexible workflow where users can quickly iterate over combinations of these components. In contrast to existing packages TyXe does not implement any layer classes, and instead relies on architectures defined in generic Pytorch code. TyXe then provides modular choices for canonical priors, variational guides, inference techniques, and layer selections for a Bayesian treatment of the specified architecture. Sampling tricks for variance reduction, such as local reparameterization or flipout, are implemented as effect handlers, which can be applied independently of other specifications. We showcase the ease of use of TyXe to explore Bayesian versions of popular models from various libraries: toy regression with a pure Pytorch neural network; large-scale image classification with torchvision ResNets; graph neural networks based on DGL; and Neural Radiance Fields built on top of Pytorch3D. Finally, we provide convenient abstractions for variational continual learning. In all cases the change from a deterministic to a Bayesian neural network comes with minimal modifications to existing code, offering a broad range of researchers and practitioners alike practical access to uncertainty estimation techniques. The library is available at https://github.com/TyXe-BDL/TyXe.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning}
}

@book{roberts2022,
  title = {The {{Principles}} of {{Deep Learning Theory}}},
	author = {Roberts, Daniel A. and Yaida, Sho and Hanin, Boris},
  year = {2022},
  eprint = {2106.10165},
  primaryclass = {hep-th, stat},
  urldate = {2023-05-19},
  abstract = {This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning,High Energy Physics - Theory,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Neural Networks\\Roberts_et_al-The_Principles_of_Deep_Learning_Theory_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\VWBC94LC\\2106.html}
}

@book{roberts2022a,
  title = {The {{Principles}} of {{Deep Learning Theory}}},
	author = {Roberts, Daniel A. and Yaida, Sho and Hanin, Boris},
  year = {2022},
  eprint = {2106.10165},
  primaryclass = {hep-th, stat},
  urldate = {2023-07-19},
  abstract = {This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning,High Energy Physics - Theory,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Roberts_et_al-The_Principles_of_Deep_Learning_Theory_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\YFH98QL7\\2106.html}
}

@article{rocco2002,
  title = {Fast {{Monte Carlo}} Reliability Evaluation Using Support Vector Machine},
	author = {Rocco, Claudio M. and Moreno, Jos{\'e} Al{\'{\i}}},
  year = {2002},
  journal = {Reliability Engineering \& System Safety},
  volume = {76},
  number = {3},
  pages = {237--243},
  urldate = {2024-01-12},
  abstract = {This paper deals with the feasibility of using support vector machine (SVM) to build empirical models for use in reliability evaluation. The approach takes advantage of the speed of SVM in the numerous model calculations typically required to perform a Monte Carlo reliability evaluation. The main idea is to develop an estimation algorithm, by training a model on a restricted data set, and replace system performance evaluation by a simpler calculation, which provides reasonably accurate model outputs. The proposed approach is illustrated by several examples. Excellent system reliability results are obtained by training a SVM with a small amount of information.},
  keywords = {Monte Carlo simulation,Reliability evaluation,Support vector machine},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\HPWNGTS8\S0951832002000157.html}
}

@inproceedings{roos2016,
  title = {Latin {{Hypercube Sampling}} Based on {{Adaptive Orthogonal Decomposition}}},
  booktitle = {Proceedings of the {{VII European Congress}} on {{Computational Methods}} in {{Applied Sciences}} and {{Engineering}} ({{ECCOMAS Congress}} 2016)},
	author = {Roos, Dirk},
  year = {2016},
  pages = {3333--3343},
  publisher = {{Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece}},
  address = {Crete Island, Greece},
  urldate = {2022-09-24},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\IMH\Roos-Latin_Hypercube_Sampling_based_on_Adaptive_Orthogonal_Decomposition_2016.pdf}
}

@article{rosenblatt1956,
  title = {Remarks on Some Nonparametric Estimates of a Density Function},
	author = {Rosenblatt, Murray},
  year = {1956},
  journal = {The Annals of Mathematical Statistics},
  volume = {27},
  number = {3},
  pages = {832--837},
}

@article{rosenbrock1960,
  title = {An {{Automatic Method}} for {{Finding}} the {{Greatest}} or {{Least Value}} of a {{Function}}},
	author = {Rosenbrock, H. H.},
  year = {1960},
  journal = {The Computer Journal},
  volume = {3},
  number = {3},
  pages = {175--184},
  urldate = {2022-01-20},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Benchmarkfunctions\Rosenbrock-An_Automatic_Method_for_Finding_the_Greatest_or_Least_Value_of_a_Function_1960.pdf}
}

@article{roy2011,
  title = {A Comprehensive Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing},
	author = {Roy, Christopher J. and Oberkampf, William L.},
  year = {2011},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {200},
  number = {25},
  pages = {2131--2144},
  urldate = {2024-01-12},
  abstract = {An overview of a comprehensive framework is given for estimating the predictive uncertainty of scientific computing applications. The framework is comprehensive in the sense that it treats both types of uncertainty (aleatory and epistemic), incorporates uncertainty due to the mathematical form of the model, and it provides a procedure for including estimates of numerical error in the predictive uncertainty. Aleatory (random) uncertainties in model inputs are treated as random variables, while epistemic (lack of knowledge) uncertainties are treated as intervals with no assumed probability distributions. Approaches for propagating both types of uncertainties through the model to the system response quantities of interest are briefly discussed. Numerical approximation errors (due to discretization, iteration, and computer round off) are estimated using verification techniques, and the conversion of these errors into epistemic uncertainties is discussed. Model form uncertainty is quantified using (a) model validation procedures, i.e., statistical comparisons of model predictions to available experimental data, and (b) extrapolation of this uncertainty structure to points in the application domain where experimental data do not exist. Finally, methods for conveying the total predictive uncertainty to decision makers are presented. The different steps in the predictive uncertainty framework are illustrated using a simple example in computational fluid dynamics applied to a hypersonic wind tunnel.},
  keywords = {Computational simulation,Modeling,Uncertainty quantification,Validation,Verification},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Validation\\Frameworks\\Roy_Oberkampf-A_comprehensive_framework_for_verification,_validation,_and_uncertainty_2011.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\4YDD696A\\S0045782511001290.html}
}

@article{roy2012,
  title = {A {{HOLISTIC APPROACH TO UNCERTAINTY QUANTIFICATION WITH APPLICATION TO SUPERSONIC NOZZLE THRUST}}},
	author = {Roy, Christopher J. and Balch, Michael S.},
  year = {2012},
  journal = {International Journal for Uncertainty Quantification},
  volume = {2},
  number = {4},
  publisher = {Begel House Inc.},
  urldate = {2023-02-04},
  abstract = {In modeling and simulation (M\&S), we seek to predict the state of a system using a computer-based simulation of a differential equation-based model. In general,...},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Density Estimation\Roy_Balch-A_HOLISTIC_APPROACH_TO_UNCERTAINTY_QUANTIFICATION_WITH_APPLICATION_TO_2012.pdf}
}

@article{rubinstein,
  title = {Simulation and the {{Monte Carlo Method}}},
	author = {Rubinstein, Reuven Y and Kroese, Dirk P},
  pages = {435},
  langid = {english},
  keywords = {Monte Carlo,Sampling},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Rubinstein_Kroese-Simulation_and_the_Monte_Carlo_Method.pdf}
}

@incollection{rumelhart1987,
  title = {Learning {{Internal Representations}} by {{Error Propagation}}},
  booktitle = {Parallel {{Distributed Processing}}: {{Explorations}} in the {{Microstructure}} of {{Cognition}}: {{Foundations}}},
	author = {Rumelhart, David E. and McClelland, James L.},
  year = {1987},
  pages = {318--362},
  publisher = {MIT Press},
  urldate = {2023-06-08},
  abstract = {This chapter contains sections titled: The Problem, The Generalized Delta Rule, Simulation Results, Some Further Generalizations, Conclusion},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\7VBJEPLV\6302929.html}
}

@article{sacks1989,
  title = {Design and {{Analysis}} of {{Computer Experiments}}},
	author = {Sacks, Jerome and Welch, William J. and Mitchell, Toby J. and Wynn, Henry P.},
  year = {1989},
  journal = {Statistical Science},
  volume = {4},
  number = {4},
  urldate = {2022-01-24},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Sacks_et_al-Design_and_Analysis_of_Computer_Experiments_1989.pdf}
}

@misc{salama2021,
  title = {Probabilistic {{Bayesian Neural Networks}}},
	author = {Salama, Kahalid},
  year = {2021},
  urldate = {2022-04-03},
  abstract = {Building probabilistic Bayesian neural network models with TensorFlow Probability.},
  howpublished = {https://keras.io/examples/keras\_recipes/bayesian\_neural\_networks/},
  langid = {english}
}

@misc{salimbeni2018,
  title = {Natural {{Gradients}} in {{Practice}}: {{Non-Conjugate Variational Inference}} in {{Gaussian Process Models}}},
  shorttitle = {Natural {{Gradients}} in {{Practice}}},
	author = {Salimbeni, Hugh and Eleftheriadis, Stefanos and Hensman, James},
  year = {2018},
  number = {arXiv:1803.09151},
  eprint = {1803.09151},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2022-08-15},
  abstract = {The natural gradient method has been used effectively in conjugate Gaussian process models, but the non-conjugate case has been largely unexplored. We examine how natural gradients can be used in non-conjugate stochastic settings, together with hyperparameter learning. We conclude that the natural gradient can significantly improve performance in terms of wall-clock time. For illconditioned posteriors the benefit of the natural gradient method is especially pronounced, and we demonstrate a practical setting where ordinary gradients are unusable. We show how natural gradients can be computed efficiently and automatically in any parameterization, using automatic differentiation. Our code is integrated into the GPflow package.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Salimbeni_et_al-Natural_Gradients_in_Practice_2018.pdf}
}

@book{saltelli2007,
  title = {Global {{Sensitivity Analysis}}. {{The Primer}}},
	author = {Saltelli, Andrea and Ratto, Marco and Andres, Terry and Campolongo, Francesca and Cariboni, Jessica and others},
  year = {2007},
  edition = {1},
  publisher = {Wiley},
  urldate = {2023-06-08},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Saltelli_et_al-Global_Sensitivity_Analysis_2007.pdf}
}

@article{salter2019,
  title = {Uncertainty {{Quantification}} for {{Computer Models With Spatial Output Using Calibration-Optimal Bases}}},
	author = {Salter, James M. and Williamson, Daniel B. and Scinocca, John and Kharin, Viatcheslav},
  year = {2019},
  journal = {Journal of the American Statistical Association},
  volume = {114},
  number = {528},
  pages = {1800--1814},
  publisher = {Taylor \& Francis},
  urldate = {2023-10-16},
  abstract = {The calibration of complex computer codes using uncertainty quantification (UQ) methods is a rich area of statistical methodological development. When applying these techniques to simulators with spatial output, it is now standard to use principal component decomposition to reduce the dimensions of the outputs in order to allow Gaussian process emulators to predict the output for calibration. We introduce the ``terminal case,'' in which the model cannot reproduce observations to within model discrepancy, and for which standard calibration methods in UQ fail to give sensible results. We show that even when there is no such issue with the model, the standard decomposition on the outputs can and usually does lead to a terminal case analysis. We present a simple test to allow a practitioner to establish whether their experiment will result in a terminal case analysis, and a methodology for defining calibration-optimal bases that avoid this whenever it is not inevitable. We present the optimal rotation algorithm for doing this, and demonstrate its efficacy for an idealized example for which the usual principal component methods fail. We apply these ideas to the CanAM4 model to demonstrate the terminal case issue arising for climate models. We discuss climate model tuning and the estimation of model discrepancy within this context, and show how the optimal rotation algorithm can be used in developing practical climate model tuning tools. Supplementary materials for this article are available online.},
  keywords = {Bayesian calibration,Climate models,History matching,Rotation,Tuning},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Dynamics\Salter_et_al-Uncertainty_Quantification_for_Computer_Models_With_Spatial_Output_Using_2019.pdf}
}

@article{sankararaman2011,
  title = {Model Validation under Epistemic Uncertainty},
	author = {Sankararaman, Shankar and Mahadevan, Sankaran},
  year = {2011},
  journal = {Reliability Engineering \& System Safety},
  volume = {96},
  number = {9},
  pages = {1232--1241},
  urldate = {2021-09-07},
  abstract = {This paper develops a methodology to assess the validity of computational models when some quantities may be affected by epistemic uncertainty. Three types of epistemic uncertainty regarding input random variables -- interval data, sparse point data, and probability distributions with parameter uncertainty -- are considered. When the model inputs are described using sparse point data and/or interval data, a likelihood-based methodology is used to represent these variables as probability distributions. Two approaches -- a parametric approach and a non-parametric approach -- are pursued for this purpose. While the parametric approach leads to a family of distributions due to distribution parameter uncertainty, the principles of conditional probability and total probability can be used to integrate the family of distributions into a single distribution. The non-parametric approach directly yields a single probability distribution. The probabilistic model predictions are compared against experimental observations, which may again be point data or interval data. A generalized likelihood function is constructed for Bayesian updating, and the posterior distribution of the model output is estimated. The Bayes factor metric is extended to assess the validity of the model under both aleatory and epistemic uncertainty and to estimate the confidence in the model prediction. The proposed method is illustrated using a numerical example.},
  langid = {english},
  keywords = {Model Validation,Validation Metric},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Sankararaman_Mahadevan-Model_validation_under_epistemic_uncertainty_2011.pdf}
}

@phdthesis{sankararaman2012,
  title = {{{UNCERTAINTY QUANTIFICATION AND INTEGRATION IN ENGINEERING SYSTEMS}}},
	author = {Sankararaman, Shankar},
  year = {2012},
  langid = {english},
  keywords = {Bayesian,Bayesian Network,Dissertation,Gaussian processes,Hierarchical Validation,Model Calibration,Model Validation,Uncertainty Quantification,Validation Metric},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\General\Sankararaman-UNCERTAINTY_QUANTIFICATION_AND_INTEGRATION_IN_ENGINEERING_SYSTEMS_2012.pdf}
}

@inproceedings{sankararaman2013,
  title = {Assessing the {{Reliability}} of {{Computational Models}} under {{Uncertainty}}},
  booktitle = {Collection of {{Technical Papers}} - {{AIAA}}/{{ASME}}/{{ASCE}}/{{AHS}}/{{ASC Structures}}, {{Structural Dynamics}} and {{Materials Conference}}},
	author = {Sankararaman, Shankar and Mahadevan, Sankaran},
  year = {2013},
  publisher = {AIAA},
  urldate = {2023-02-06},
  keywords = {Boundary Value Problems,Computing,Heat Conduction,Hysteresis,Monte Carlo Analysis,Numerical Modeling,Probability Density Functions,Steady State Heat Transfer,Thermal Conductivity},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Sankararaman_Mahadevan-Assessing_the_Reliability_of_Computational_Models_under_Uncertainty_2013.pdf}
}

@article{sankararaman2013a,
  title = {Test {{Resource Allocation}} in {{Hierarchical Systems Using Bayesian Networks}}},
	author = {Sankararaman, Shankar and McLemore, Kyle and Mahadevan, Sankaran and Bradford, Samuel Case and Peterson, Lee D.},
  year = {2013},
  journal = {AIAA Journal},
  volume = {51},
  number = {3},
  pages = {537--550},
  publisher = {{American Institute of Aeronautics and Astronautics}},
  urldate = {2023-03-11},
  abstract = {This paper develops analytical methods for test resource allocation that aid in reducing the uncertainty in the system model prediction for multilevel and multidisciplinary systems. The various component, subsystem, and system-level model predictions; the corresponding inputs and calibration parameters; test data; and model and measurement errors are connected efficiently using a Bayesian network. This provides a unified framework for uncertainty analysis where test data can be integrated along with computational simulations. The Bayesian network is used in an inverse problem where the model parameters of multiple subsystems are calibrated simultaneously. This leads to a decrease in the variance of the model parameters, and hence, in the variance of the overall system performance prediction. An optimization-based procedure is then used for test resource allocation using the Bayesian network, and those tests that can effectively reduce the uncertainty in the system model prediction are identified. The proposed methods are extended to three types of aerospace systems-testing applications: structural dynamics (multilevel), thermally induced vibration/flutter (multidisciplinary), and simplified space telescope mirror (multilevel, multidisciplinary).},
  keywords = {Aerospace System Testing,Bayesian Networks,Elastic Modulus,Inverse Problems,Numerical Integration,Probability Density Functions,Sensitivity Analysis,Space Telescopes,Structural Dynamics,Telescopes}
}

@article{sankararaman2015,
  title = {Integration of Model Verification, Validation, and Calibration for Uncertainty Quantification in Engineering Systems},
	author = {Sankararaman, Shankar and Mahadevan, Sankaran},
  year = {2015},
  journal = {Reliability Engineering \& System Safety},
  volume = {138},
  pages = {194--209},
  urldate = {2023-11-15},
  abstract = {This paper proposes a Bayesian methodology to integrate model verification, validation, and calibration activities for the purpose of overall uncertainty quantification in different types of engineering systems. The methodology is first developed for single-level models, and then extended to systems that are studied using multi-level models that interact with each other. Two types of interactions amongst multi-level models are considered: (1) Type-I, where the output of a lower-level model (component and/or subsystem) becomes an input to a higher level system model, and (2) Type-II, where parameters of the system model are inferred using lower-level models and tests (that describe simplified components and/or isolated physics). The various models, their inputs, parameters, and outputs, experimental data, and various sources of model error are connected through a Bayesian network. The results of calibration, verification, and validation with respect to each individual model are integrated using the principles of conditional probability and total probability, and propagated through the Bayesian network in order to quantify the overall system-level prediction uncertainty. The proposed methodology is illustrated with numerical examples that deal with heat conduction and structural dynamics.},
  keywords = {Bayesian network,Calibration,Multi-level system,Uncertainty quantification,Validation,Verification},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Validation\\General\\Sankararaman_Mahadevan-Integration_of_model_verification,_validation,_and_calibration_for_uncertainty_2015.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\ZC8YHWCE\\S0951832015000332.html}
}

@inproceedings{sargent2010,
  title = {Verification and Validation of Simulation Models},
  booktitle = {Proceedings of the 2010 {{Winter Simulation Conference}}},
	author = {Sargent, Robert G.},
  year = {2010},
  pages = {166--183},
  publisher = {IEEE},
  address = {Baltimore, MD, USA},
  urldate = {2021-09-07},
  abstract = {In this paper we discuss verification and validation of simulation models. Four different approaches to deciding model validity are described, a graphical paradigm that relates verification and validation to the model development process is presented, and various validation techniques are defined. Conceptual model validity, model verification, operational validity, and data validity are discussed and a way to document results is given. A recommended procedure for model validation is presented and model accreditation is briefly discussed.},
  langid = {english},
  keywords = {Model Validation},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\General\Sargent-Verification_and_validation_of_simulation_models_2010.pdf}
}

@inproceedings{sargent2016,
  title = {A Tutorial on the Operational Validation of Simulation Models},
  booktitle = {2016 {{Winter Simulation Conference}} ({{WSC}})},
	author = {Sargent, Robert G. and Goldsman, David M. and Yaacoub, Tony},
  year = {2016},
  pages = {163--177},
  publisher = {IEEE},
  address = {Washington, DC, USA},
  urldate = {2021-09-07},
  abstract = {This tutorial discusses in depth the operational validation of simulation models after a brief overview of verification and validation of simulation models. The discussion of operational validation first covers the different approaches used for observable and non-observable systems. Next, various types of graphical displays of model output behavior are presented; this is followed by how these displays can be used in determining model validity by the model developers, subject matter experts, and others when no system data are available; and how these displays can be used as reference distributions for operational validation when system data are available. Lastly, the use of the ``interval hypothesis test'' is covered for operational validation when sufficient system data are available. Various examples are presented.},
  langid = {english},
  keywords = {Model Validation,Simulation Models,Tutorial},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\General\Sargent_et_al-A_tutorial_on_the_operational_validation_of_simulation_models_2016.pdf}
}

@article{sauer2023,
  title = {Vecchia-{{Approximated Deep Gaussian Processes}} for {{Computer Experiments}}},
	author = {Sauer, Annie and Cooper, Andrew and Gramacy, Robert B.},
  year = {2023},
  journal = {Journal of Computational and Graphical Statistics},
  volume = {32},
  number = {3},
  pages = {824--837},
  publisher = {Taylor \& Francis},
  urldate = {2023-10-19},
  abstract = {Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model nonstationary dynamics. Two DGP regimes have emerged in recent literature. A ``big data'' regime, prevalent in machine learning, favors approximate, optimization-based inference for fast, high-fidelity prediction. A ``small data'' regime, preferred for computer surrogate modeling, deploys posterior integration for enhanced uncertainty quantification (UQ). We aim to bridge this gap by expanding the capabilities of Bayesian DGP posterior inference through the incorporation of the Vecchia approximation, allowing linear computational scaling without compromising accuracy or UQ. We are motivated by surrogate modeling of simulation campaigns with upwards of 100,000 runs---a size too large for previous fully-Bayesian implementations---and demonstrate prediction and UQ superior to that of ``big data'' competitors. All methods are implemented in the deepgp package on CRAN. Supplementary materials for this article are available online.},
  keywords = {Nearest neighbor,Nonstationary,Sparse matrix,Surrogate,Uncertainty quantification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Deep GP\Sauer_et_al-Vecchia-Approximated_Deep_Gaussian_Processes_for_Computer_Experiments_2023.pdf}
}

@article{sauer2023a,
  title = {Active {{Learning}} for {{Deep Gaussian Process Surrogates}}},
	author = {Sauer, Annie and Gramacy, Robert B. and Higdon, David},
  year = {2023},
  journal = {Technometrics},
  volume = {65},
  number = {1},
  pages = {4--18},
  publisher = {Taylor \& Francis},
  urldate = {2023-10-19},
  abstract = {Deep Gaussian processes (DGPs) are increasingly popular as predictive models in machine learning for their nonstationary flexibility and ability to cope with abrupt regime changes in training data. Here, we explore DGPs as surrogates for computer simulation experiments whose response surfaces exhibit similar characteristics. In particular, we transport a DGP's automatic warping of the input space and full uncertainty quantification, via a novel elliptical slice sampling Bayesian posterior inferential scheme, through to active learning strategies that distribute runs nonuniformly in the input space---something an ordinary (stationary) GP could not do. Building up the design sequentially in this way allows smaller training sets, limiting both expensive evaluation of the simulator code and mitigating cubic costs of DGP inference. When training data sizes are kept small through careful acquisition, and with parsimonious layout of latent layers, the framework can be both effective and computationally tractable. Our methods are illustrated on simulation data and two real computer experiments of varying input dimensionality. We provide an open source implementation in the deepgp package on CRAN.},
  keywords = {Computer model,Elliptical slice sampling,Emulator,Kriging,Sequential design},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Deep GP\Sauer_et_al-Active_Learning_for_Deep_Gaussian_Process_Surrogates_2023.pdf}
}

@article{saul,
  title = {Chained {{Gaussian Processes}}},
	author = {Saul, Alan D and Hensman, James and Vehtari, Aki and Lawrence, Neil D},
  abstract = {Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to an linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models Chained Gaussian Processes: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\NW7Q5JKZ\Saul et al. - Chained Gaussian Processes.pdf}
}

@misc{saul2016,
  title = {Chained {{Gaussian Processes}}},
	author = {Saul, Alan D. and Hensman, James and Vehtari, Aki and Lawrence, Neil D.},
  year = {2016},
  number = {arXiv:1604.05263},
  eprint = {1604.05263},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-06-28},
  abstract = {Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to a linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models Chained Gaussian Processes: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e. a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Saul_et_al-Chained_Gaussian_Processes_2016.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\VQAMPKAG\\1604.html}
}

@article{saula,
  title = {Chained {{Gaussian Processes}}},
	author = {Saul, Alan D and Hensman, James and Vehtari, Aki and Lawrence, Neil D},
  abstract = {Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to an linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models Chained Gaussian Processes: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\S9AKUBB9\Saul et al. - Chained Gaussian Processes.pdf}
}

@article{saulb,
  title = {Chained {{Gaussian Processes}}},
	author = {Saul, Alan D and Hensman, James and Vehtari, Aki and Lawrence, Neil D},
  abstract = {Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to an linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models Chained Gaussian Processes: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\6AGFKSAD\Saul et al. - Chained Gaussian Processes.pdf}
}

@article{saulc,
  title = {Chained {{Gaussian Processes}}},
	author = {Saul, Alan D and Hensman, James and Vehtari, Aki and Lawrence, Neil D},
  abstract = {Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to an linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models Chained Gaussian Processes: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\A97AEWPE\Saul et al. - Chained Gaussian Processes.pdf}
}

@inproceedings{scheffer2001,
  title = {Active Hidden Markov Models for Information Extraction},
  booktitle = {Advances in {{Intelligent Data Analysis}}},
	author = {Scheffer, Tobias and Decomain, Christian and Wrobel, Stefan},
  year = {2001},
  pages = {309--318},
  publisher = {Springer Berlin Heidelberg},
  address = {Berlin, Heidelberg},
  abstract = {Information extraction from HTML documents requires a classifier capable of assigning semantic labels to the words or word sequences to be extracted. If completely labeled documents are available for training, well-known Markov model techniques can be used to learn such classifiers. In this paper, we consider the more challenging task of learning hidden Markov models (HMMs) when only partially (sparsely) labeled documents are available for training. We first give detailed account of the task and its appropriate loss function, and show how it can be minimized given an HMM. We describe an EM style algorithm for learning HMMs from partially labeled data. We then present an active learning algorithm that selects ``difficult'' unlabeled tokens and asks the user to label them. We study empirically by how much active learning reduces the required data labeling effort, or increases the quality of the learned model achievable with a given amount of user effort.},
}

@article{schmidhuber2015,
  title = {Deep {{Learning}} in {{Neural Networks}}: {{An Overview}}},
  shorttitle = {Deep {{Learning}} in {{Neural Networks}}},
	author = {Schmidhuber, Juergen},
  year = {2015},
  journal = {Neural Networks},
  volume = {61},
  eprint = {1404.7828},
  pages = {85--117},
  urldate = {2022-01-21},
  abstract = {In recent years, deep artificial neural networks (including recurrent ones) have won numerous contests in pattern recognition and machine learning. This historical survey compactly summarises relevant work, much of it from the previous millennium. Shallow and deep learners are distinguished by the depth of their credit assignment paths, which are chains of possibly learnable, causal links between actions and effects. I review deep supervised learning (also recapitulating the history of backpropagation), unsupervised learning, reinforcement learning \& evolutionary computation, and indirect search for short programs encoding deep and large networks.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Computer Science - Neural and Evolutionary Computing}
}

@article{scholkopf,
  title = {Kernel {{Principal Component Analysis}}},
	author = {Sch{\"o}lkopf, Bernhard and Smola, Alex J. and Muller, Klaus Robert},
  abstract = {A new method for performing a nonlinear form of Principal Component Analysis is proposed. By the use of integral operator kernel functions, one can e ciently compute principal components in high dimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible d pixel products in images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition.},
  langid = {english}
}

@inproceedings{scholkopf1997,
  title = {Kernel Principal Component Analysis},
  booktitle = {Artificial {{Neural Networks}} --- {{ICANN}}'97},
	author = {Sch{\"o}lkopf, Bernhard and Smola, Alexander and M{\"u}ller, Klaus-Robert},
  year = {1997},
  series = {Lecture {{Notes}} in {{Computer Science}}},
  pages = {583--588},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  abstract = {A new method for performing a nonlinear form of Principal Component Analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible d-pixel products in images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition.},
  langid = {english},
  keywords = {Feature Space,Independent Component Analysis,Kernel Principal Component Analysis,Standard Principal Component Analysis,Support Vector Machine},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\BG4DVPCI\Scholkopf et al. - Kernel Principal Component Analysis.pdf}
}

@misc{scholkopf2021,
  title = {Towards {{Causal Representation Learning}}},
	author = {Sch{\"o}lkopf, Bernhard and Locatello, Francesco and Bauer, Stefan and Ke, Nan Rosemary and Kalchbrenner, Nal and others},
  year = {2021},
  number = {arXiv:2102.11107},
  eprint = {2102.11107},
  primaryclass = {cs},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {The two fields of machine learning and graphical causality arose and developed separately. However, there is now cross-pollination and increasing interest in both fields to benefit from the advances of the other. In the present paper, we review fundamental concepts of causal inference and relate them to crucial open problems of machine learning, including transfer and generalization, thereby assaying how causality can contribute to modern machine learning research. This also applies in the opposite direction: we note that most work in causality starts from the premise that the causal variables are given. A central problem for AI and causality is, thus, causal representation learning, the discovery of high-level causal variables from low-level observations. Finally, we delineate some implications of causality for machine learning and propose key research areas at the intersection of both communities.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Causal Inference\\Scholkopf_et_al-Towards_Causal_Representation_Learning_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\AHY9JH8P\\2102.html}
}

@misc{schultz2022,
  title = {Deep {{Learning Gaussian Processes For Computer Models}} with {{Heteroskedastic}} and {{High-Dimensional Outputs}}},
	author = {Schultz, Laura and Sokolov, Vadim},
  year = {2022},
  number = {arXiv:2209.02163},
  eprint = {2209.02163},
  primaryclass = {stat},
  publisher = {arXiv},
  urldate = {2023-10-19},
  abstract = {Deep Learning Gaussian Processes (DL-GP) are proposed as a methodology for analyzing (approximating) computer models that produce heteroskedastic and high-dimensional output. Computer simulation models have many areas of applications, including social-economic processes, agriculture, environmental, biology, engineering and physics problems. A deterministic transformation of inputs is performed by deep learning and predictions are calculated by traditional Gaussian Processes. We illustrate our methodology using a simulation of motorcycle accidents and simulations of an Ebola outbreak. Finally, we conclude with directions for future research.},
  archiveprefix = {arxiv},
  keywords = {Statistics - Applications},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Schultz_Sokolov-Deep_Learning_Gaussian_Processes_For_Computer_Models_with_Heteroskedastic_and_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\RTSFSSU3\\2209.html}
}

@book{schwefel1981,
  title = {Numerical Optimization of Computer Models},
	author = {Schwefel, H.P.},
  year = {1981},
  publisher = {John Wiley Sons}
}

@article{schwefel2007,
  title = {Numerical Optimization of Computer Models, {{Hans-Paul Schwefel}}, {{Wiley}}, {{Chichester}}, 1981. {{Price}}: {\pounds}12.50},
  shorttitle = {Numerical Optimization of Computer Models, {{Hans-Paul Schwefel}}, {{Wiley}}, {{Chichester}}, 1981. {{Price}}},
	author = {Schwefel, H.P.},
  year = {2007},
  journal = {Optimal Control Applications and Methods},
  volume = {3},
  number = {1},
  pages = {97--97},
  urldate = {2022-03-16},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\EMPTY_COLLECTION_NAME\Schwefel-Numerical_optimization_of_computer_models,_Hans-Paul_Schwefel,_Wiley,_2007.pdf}
}

@techreport{settles2010,
  type = {Technical {{Report}}},
  title = {Active {{Learning Literature Survey}}},
	author = {Settles, Burr},
  year = {2010},
  institution = {University of Wisconsin-Madison Department of Computer Sciences},
  urldate = {2023-12-20},
  abstract = {The key idea behind active learning is that a machine learning algorithm can achieve greater accuracy with fewer labeled training instances if it is allowed to choose the training data from which is learns. An active learner may ask queries in the form of unlabeled instances to be labeled by an oracle (e.g., a human annotator). Active learning is well-motivated in many modern machine learning problems, where unlabeled data may be abundant but labels are difficult, time-consuming, or expensive to obtain.  This report provides a general introduction to active learning and a survey of the literature. This includes a discussion of the scenarios in which queries can be formulated, and an overview of the query strategy frameworks proposed in the literature to date. An analysis of the empirical and theoretical evidence for active learning, a summary of several problem setting variants, and a discussion of related topics in machine learning research are also presented.},
  langid = {english},
  annotation = {Accepted: 2012-03-15T17:23:56Z},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Adaptive Methods\Settles-Active_Learning_Literature_Survey_2009.pdf}
}

@article{sewall1921,
  title = {Correlation and Causation},
	author = {Sewall, Wright},
  year = {1921},
  journal = {Journal of Agricultural Research},
  volume = {20},
  number = {3},
  pages = {557--585},
}

@article{shlens,
  title = {A {{Tutorial}} on {{Principal Component Analysis}}},
	author = {Shlens, Jonathon},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\WYZBYJAI\Shlens - A Tutorial on Principal Component Analysis.pdf}
}

@misc{shlens2014,
  title = {A {{Tutorial}} on {{Principal Component Analysis}}},
	author = {Shlens, Jonathon},
  year = {2014},
  number = {arXiv:1404.1100},
  eprint = {1404.1100},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-06-12},
  abstract = {Principal component analysis (PCA) is a mainstay of modern data analysis - a black box that is widely used but (sometimes) poorly understood. The goal of this paper is to dispel the magic behind this black box. This manuscript focuses on building a solid intuition for how and why principal component analysis works. This manuscript crystallizes this knowledge by deriving from simple intuitions, the mathematics behind PCA. This tutorial does not shy away from explaining the ideas informally, nor does it shy away from the mathematics. The hope is that by addressing both aspects, readers of all levels will be able to gain a better understanding of PCA as well as the when, the how and the why of applying this technique.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Shlens-A_Tutorial_on_Principal_Component_Analysis_2014.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\QWJKN4E4\\1404.html}
}

@article{silagadze2007,
  title = {Finding Two-Dimensional Peaks},
	author = {Silagadze, Z. K.},
  year = {2007},
  journal = {Physics of Particles and Nuclei Letters},
  volume = {4},
  number = {1},
  pages = {73--80},
  urldate = {2022-01-20},
  langid = {english}
}

@book{smith2013,
  title = {Uncertainty Quantification: Theory, Implementation, and Applications},
  shorttitle = {Uncertainty Quantification},
	author = {Smith, Ralph C.},
  year = {2013},
  series = {Computational Science and Engineering Series},
  publisher = {{Society for Industrial and Applied Mathematics}},
  address = {Philadelphia},
  lccn = {QA276.8 .S64 2013},
  keywords = {Estimation theory,Measurement uncertainty (Statistics)},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Uncertainty Quantification\Smith-Uncertainty_quantification_2013.pdf}
}

@article{smola2004,
  title = {A Tutorial on Support Vector Regression},
	author = {Smola, Alex J. and Sch{\"o}lkopf, Bernhard},
  year = {2004},
  journal = {Statistics and Computing},
  volume = {14},
  number = {3},
  pages = {199--222},
  urldate = {2022-01-21},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Smola_Scholkopf-A_tutorial_on_support_vector_regression_2004.pdf}
}

@inproceedings{snoek2012,
  title = {Practical {{Bayesian Optimization}} of {{Machine Learning Algorithms}}},
  booktitle = {Advances in {{Neural Information Processing Systems}}},
	author = {Snoek, Jasper and Larochelle, Hugo and Adams, Ryan P},
  year = {2012},
  volume = {25},
  publisher = {Curran Associates, Inc.},
  urldate = {2024-01-28},
  abstract = {The use of machine learning algorithms frequently involves careful tuning of learning parameters and model hyperparameters. Unfortunately, this tuning is often a ``black art'' requiring expert experience, rules of thumb, or sometimes brute-force search. There is therefore great appeal for automatic approaches that can optimize the performance of any given learning algorithm to the problem at hand. In this work, we consider this problem through the framework of Bayesian optimization, in which a learning algorithm's generalization performance is modeled as a sample from a Gaussian process (GP). We show that certain choices for the nature of the GP, such as the type of kernel and the treatment of its hyperparameters, can play a crucial role in obtaining a good optimizer that can achieve expert-level performance. We describe new algorithms that take into account the variable cost (duration) of learning algorithm experiments and that can leverage the presence of multiple cores for parallel experimentation. We show that these proposed algorithms improve on previous automatic procedures and can reach or surpass human expert-level optimization for many algorithms including Latent Dirichlet Allocation, Structured SVMs and convolutional neural networks.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Optimization\BO\Snoek_et_al-Practical_Bayesian_Optimization_of_Machine_Learning_Algorithms_2012.pdf}
}

@article{spinti2021,
  title = {Using {{Bayesian Analysis}} to {{Quantify Uncertainty}} in {{Radiometer Measurements}}},
	author = {Spinti, Jennifer P. and Smith, Sean T. and Smith, Philip J. and Harding, N. Stanley and Scheib, Kaitlyn and others},
  year = {2021},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {6},
  number = {1},
  pages = {011003},
  urldate = {2021-09-07},
  abstract = {Abstract             We apply Bayesian inference to instrument calibration and experimental-data uncertainty analysis for the specific application of measuring radiative intensity with a narrow-angle radiometer. We develop a physics-based instrument model that describes temporally varying radiative intensity, the indirectly measured quantity of interest, as a function of scenario and model parameters. We identify a set of five uncertain parameters, find their probability distributions (the posterior or inverse problem) given the calibration data by applying Bayes' Theorem, and employ a local linearization to marginalize the nuisance parameters resulting from errors-in-variables. We then apply the instrument model to a new scenario that is the intended use of the instrument, a 1.5\,MW coal-fired furnace. Unlike standard error propagation, this Bayesian method infers values for the five uncertain parameters by sampling from the posterior distribution and then computing the intensity with quantifiable uncertainty at the point of a new, in situ furnace measurement (the posterior predictive or forward problem). Given the instrument-model context of this analysis, the propagated uncertainty provides a significant proportion of the measurement error for each in situ furnace measurement. With this approach, we produce uncertainties at each temporal measurement of the radiative intensity in the furnace, successfully identifying temporal variations that were otherwise indistinguishable from measurement uncertainty.},
  langid = {english},
  keywords = {Bayesian,Model Validation},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Applied Model Validation\Spinti_et_al-Using_Bayesian_Analysis_to_Quantify_Uncertainty_in_Radiometer_Measurements_2021.pdf}
}

@article{spitieris2023,
  title = {Bayesian {{Calibration}} of {{Imperfect Computer Models}} Using {{Physics-Informed Priors}}},
	author = {Spitieris, Michail and Steinsland, Ingelin},
  year = {2023},
  journal = {Journal of Machine Learning Research},
  volume = {24},
  number = {108},
  pages = {1--39},
  urldate = {2023-10-18},
  abstract = {We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed priors, which are multi-output GP priors that encode the model's structure in the covariance function. This is extended into a fully Bayesian framework that quantifies the uncertainty of physical parameters and model predictions. Since physical models often are imperfect descriptions of the real process, we allow the model to deviate from the observed data by considering a discrepancy function. For inference Hamiltonian Monte Carlo is used. Further, approximations for big data are developed that reduce the computational complexity from  O( N 3 ) {$O$} ( {$N$} 3 )  to  O(N{$\cdot$} m 2 ), {$O$} ( {$N$} {$\cdot$} {$m$} 2 ) ,  where  m{$\ll$}N. {$m$} {$\ll$} {$N$} .  Our approach is demonstrated in simulation and real data case studies where the physics are described by time-dependent ODEs (cardiovascular models) and space-time dependent PDEs (heat equation). In the studies, it is shown that our modelling framework can recover the true parameters of the physical models in cases where 1) the reality is more complex than our modelling choice and 2) the data acquisition process is biased while also producing accurate predictions. Furthermore, it is demonstrated that our approach is computationally faster than traditional Bayesian calibration methods.},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\DBC\\KOH\\Spitieris_Steinsland-Bayesian_Calibration_of_Imperfect_Computer_Models_using_Physics-Informed_Priors_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\L27HA56L\\BC-with-PI-priors.html}
}

@inproceedings{stanton2023,
  title = {Bayesian {{Optimization}} with {{Conformal Prediction Sets}}},
  booktitle = {Proceedings of {{The}} 26th {{International Conference}} on {{Artificial Intelligence}} and {{Statistics}}},
	author = {Stanton, Samuel and Maddox, Wesley and Wilson, Andrew Gordon},
  year = {2023},
  pages = {959--986},
  publisher = {PMLR},
  urldate = {2024-03-05},
  abstract = {Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Conformal Prediction\Stanton_et_al-Bayesian_Optimization_with_Conformal_Prediction_Sets_2023.pdf}
}

@book{stein1999,
  title = {Interpolation of {{Spatial Data}}},
	author = {Stein, Michael L.},
  year = {1999},
  series = {Springer {{Series}} in {{Statistics}}},
  publisher = {Springer},
  address = {New York},
  urldate = {2022-03-12},
}

@inproceedings{sterling2015,
  title = {Welding Parameter Optimization Based on {{Gaussian}} Process Regression {{Bayesian}} Optimization Algorithm},
  booktitle = {2015 {{IEEE International Conference}} on {{Automation Science}} and {{Engineering}} ({{CASE}})},
	author = {Sterling, Dillon and Sterling, Tyler and Zhang, YuMing and Chen, Heping},
  year = {2015},
  pages = {1490--1496},
  publisher = {IEEE},
  address = {Gothenburg, Sweden},
  urldate = {2022-03-04},
}

@article{styblinski1990,
  title = {Experiments in {{Nonconvex Optimization}}: {{Stochastic Approximation}} with {{Function Smoothing}} and {{Simulated Annealing}}},
	author = {Styblinski, M. and Tang, T.},
  year = {1990},
  journal = {Neural Networks},
  volume = {3},
  number = {4},
  pages = {467--483}
}

@article{styblinski1990a,
  title = {Experiments in Nonconvex Optimization: {{Stochastic}} Approximation with Function Smoothing and Simulated Annealing},
  shorttitle = {Experiments in Nonconvex Optimization},
	author = {Styblinski, M.A. and Tang, T.-S.},
  year = {1990},
  journal = {Neural Networks},
  volume = {3},
  number = {4},
  pages = {467--483},
  urldate = {2022-01-21},
  langid = {english}
}

@phdthesis{sudret2005,
  title = {Uncertainty Propagation and Sensitivity Analysis in Mechanical Models},
	author = {Sudret, Bruno},
  year = {2005},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Uncertainty Quantification\Sudret-Uncertainty_propagation_and_sensitivity_analysis_in_mechanical_models_2005.pdf}
}

@article{sundararajan2001,
  title = {Predictive {{Approaches}} for {{Choosing Hyperparameters}} in {{Gaussian Processes}}},
	author = {Sundararajan, S. and Keerthi, S. S.},
  year = {2001},
  journal = {Neural Computation},
  volume = {13},
  number = {5},
  pages = {1103--1118},
  urldate = {2022-02-14},
  abstract = {Gaussian processes are powerful regression models specified by parameterized mean and covariance functions. Standard approaches to choose these parameters (known by the name hyperparameters) are maximum likelihood and maximum a posteriori. In this article, we propose and investigate predictive approaches based on Geisser's predictive sample reuse (PSR) methodology and the related Stone's cross-validation (CV) methodology. More specifically, we derive results for Geisser's surrogate predictive probability (GPP), Geisser's predictive mean square error (GPE), and the standard CV error and make a comparative study. Within an approximation we arrive at the generalized cross-validation (GCV) and establish its relationship with the GPP and GPE approaches. These approaches are tested on a number of problems. Experimental results show that these approaches are strongly competitive with the existing approaches.},
  langid = {english}
}

@article{surer2023,
  title = {Sequential {{Bayesian}} Experimental Design for Calibration of Expensive Simulation Models},
	author = {S{\"u}rer, {\"O}zge and Plumlee, Matthew and Wild, Stefan M.},
  year = {2023},
  journal = {Technometrics},
  volume = {0},
  number = {ja},
  pages = {1--26},
  publisher = {Taylor \& Francis},
  urldate = {2023-09-18},
  abstract = {Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at different parameter settings. Using intelligent and adaptive selection of parameters to build the emulator can drastically improve the efficiency of the calibration process. The article proposes a sequential framework with a novel criterion for parameter selection that targets learning the posterior density of the parameters. The emergent behavior from this criterion is that exploration happens by selecting parameters in uncertain posterior regions while simultaneously exploitation happens by selecting parameters in regions of high posterior density. The advantages of the proposed method are illustrated using several simulation experiments and a nuclear physics reaction model.},
  keywords = {Acquisition,Active learning,Emulation,Gaussian process,Uncertainty quantification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Surer_et_al-Sequential_Bayesian_experimental_design_for_calibration_of_expensive_simulation_2023.pdf}
}

@article{tang2023,
  title = {{{DAS-PINNs}}: {{A}} Deep Adaptive Sampling Method for Solving High-Dimensional Partial Differential Equations},
  shorttitle = {{{DAS-PINNs}}},
	author = {Tang, Kejun and Wan, Xiaoliang and Yang, Chao},
  year = {2023},
  journal = {Journal of Computational Physics},
  volume = {476},
  pages = {111868},
  urldate = {2023-06-12},
  abstract = {In this work we propose a deep adaptive sampling (DAS-PINNs) method for solving partial differential equations (PDEs), where deep neural networks are utilized to approximate the solutions of PDEs and deep generative models are employed to generate new collocation points to refine the training set. The overall procedure of DAS consists of two components: solving the PDEs by minimizing the residual loss on the collocation points in the training set and generating a new training set to further improve the accuracy of the current approximate solution. In particular, we treat the residual as a probability density function and approximate it with a deep generative model, called KRnet. The new samples from KRnet are consistent with the distribution induced by the residual, i.e., more samples are located in the region of large residual and less samples are located in the region of small residual. Analogous to classical adaptive methods such as the adaptive finite element, KRnet acts as an error indicator that guides the refinement of the training set. Compared to the neural network approximation obtained with uniformly distributed collocation points, the developed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems. We demonstrate the effectiveness of the proposed DAS-PINNs method with numerical experiments.},
  langid = {english},
  keywords = {Adaptive sampling,Deep generative models,Deep learning,Numerical approximation of PDEs},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Design of Experiments\\Adaptive Methods\\Tang_et_al-DAS-PINNs_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\LXPRT4EY\\S0021999122009317.html}
}

@article{tauscher2024,
  title = {Bayesian Calibration of Ball Grid Array Lifetime Models for Solder Fatigue},
	author = {Tauscher, Markus and L{\"a}mmle, Sven and Roos, Dirk and Wilde, J{\"u}rgen},
  year = {2024},
  journal = {Microelectronics Reliability},
  volume = {155},
  pages = {115366},
  abstract = {One of the primary failure modes for solder joints is caused by temperature cycling of the component. The induced stress causes creeping which leads to crack initiation and propagation until failure. Finite element analysis can be used to simulate occurring creep-strain for different temperatures and geometries. Subsequently, creep-strain is used as damage parameter together with a lifetime model to estimate the reliability of the component. Economic factors constrain data available for calibration of the lifetime model, leading to uncertainties in parameter estimates and reliability. Therefore, we propose a model calibration method for solder fatigue with the Coffin--Manson lifetime model based on Bayesian inference. The approach is able to incorporate respective uncertainties from data variability and sparsity, and takes prior knowledge into account. We show how to obtain reliability estimates from the calibrated model considering uncertainties from parameter estimation. Furthermore, we apply the Bayesian calibration method to experimental data obtained from ball-grid arrays with lead-free SAC305 solder joints. In our ablation study we show that our approach is more robust and accurate upon the prevalent calibration method used, especially if only limited data is available.},
  keywords = {Bayesian inference,BGA,Calibration,Coffin-Manson,Micro-electronic device},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\IMH\Tauscher_et_al-Bayesian_calibration_of_ball_grid_array_lifetime_models_for_solder_fatigue_2024.pdf}
}

@article{teixeira2021,
  title = {Adaptive Approaches in Metamodel-Based Reliability Analysis: {{A}} Review},
  shorttitle = {Adaptive Approaches in Metamodel-Based Reliability Analysis},
	author = {Teixeira, Rui and Nogal, Maria and O'Connor, Alan},
  year = {2021},
  journal = {Structural Safety},
  volume = {89},
  pages = {102019},
  urldate = {2024-01-03},
  abstract = {The present work reviews the implementation of adaptive metamodeling for reliability analysis with emphasis in four main types of metamodels: response surfaces, polynomial chaos expansions, support vector machines, and Kriging models. The discussion presented is motivated by the identified spread and little interaction between metamodeling techniques in reliability, which makes it challenging for practitioners to decide which one to consider in a context of implementation. The conceptual problem of reliability analysis and the theoretical description of the four models is presented, and complemented by a comparative discussion of applications with identification of new areas of interest. The different considerations that influence the efficiency of adaptive metamodeling are reviewed, with extension to applicability discussions for the four models researched. Despite all adaptive techniques contributing to achieve significant gains in the amount of effort required for reliability analysis, and with minimal trade-off in accuracy, they should not be expected to perform equally in regard to the dependence on the reliability problem being addressed. Cross application of methodologies, bridging the gap between methodology and application, and ensembles are some of new areas of research interest identified. One of the major critical considerations for adaptive metamodeling, and that has been target of limited research, is the need for comprehensive techniques that allow a blind selection of the most adequate model with relation to the problem in--hand. To conclude, the extensive and comprehensive discussion presented aims to be a first step for the unification of the field of adaptive metamodeling in reliability; so that future implementations do not exclusively follow individual lines of research that progressively become more narrow in scope, but also seek transversal developments in the field of adaptive metamodeling for reliability analysis.},
  keywords = {Adaptive metamodeling,Kriging,Polynomial chaos expansion,Reliability analysis,Response surfaces,Support vector machines},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Reliability Analysis\\Teixeira_et_al-Adaptive_approaches_in_metamodel-based_reliability_analysis_2021.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\NCPUH5I8\\S0167473020300989.html}
}

@article{thelen2022,
  title = {A Comprehensive Review of Digital Twin~---~Part 1: Modeling and Twinning Enabling Technologies},
  shorttitle = {A Comprehensive Review of Digital Twin~---~Part 1},
	author = {Thelen, Adam and Zhang, Xiaoge and Fink, Olga and Lu, Yan and Ghosh, Sayan and others},
  year = {2022},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {65},
  number = {12},
  pages = {354},
  urldate = {2023-10-16},
  abstract = {As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This first paper presents a thorough literature review of digital twin trends across many disciplines currently pursuing this area of research. Then, digital twin modeling and twinning enabling technologies are further analyzed by classifying them into two main categories: physical-to-virtual, and virtual-to-physical, based on the direction in which data flows. Finally, this paper provides perspectives on the trajectory of digital twin technology over the next decade, and introduces a few emerging areas of research which will likely be of great use in future digital twin research. In part two of this review, the role of uncertainty quantification and optimization are discussed, a battery digital twin is demonstrated, and more perspectives on the future of digital twin are shared.~Code and preprocessed data for generating all the results and figures presented in the battery digital twin~case study in part 2 of this review~are available on Github.},
  langid = {english},
  keywords = {Digital twin,Enabling technology,Industry 4.0,Machine learning,Optimization,Perspective,Review},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Digital Twin\Thelen_et_al-A_comprehensive_review_of_digital_twin_—_part_1_2022.pdf}
}

@article{thelen2022a,
  title = {A Comprehensive Review of Digital Twin---Part 2: Roles of Uncertainty Quantification and Optimization, a Battery Digital Twin, and Perspectives},
  shorttitle = {A Comprehensive Review of Digital Twin---Part 2},
	author = {Thelen, Adam and Zhang, Xiaoge and Fink, Olga and Lu, Yan and Ghosh, Sayan and others},
  year = {2022},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {66},
  number = {1},
  pages = {1},
  urldate = {2023-10-16},
  abstract = {As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision- and policy-making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This second paper presents a literature review of key enabling technologies of digital twins, with an emphasis on uncertainty quantification, optimization methods, open-source datasets and tools, major findings, challenges, and future directions. Discussions focus on current methods of uncertainty quantification and optimization and how they are applied in different dimensions of a digital twin. Additionally, this paper presents a case study where a battery digital twin is constructed and tested to illustrate some of the modeling and twinning methods reviewed in this two-part review. Code and preprocessed data for generating all the results and figures presented in the case study are available on Github.},
  langid = {english},
  keywords = {Digital twin,Enabling technology,Industry 4.0,Machine learning,Optimization,Perspective,Review},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Digital Twin\Thelen_et_al-A_comprehensive_review_of_digital_twin—part_2_2022.pdf}
}

@book{theodoridis2020,
  title = {Machine Learning: A {{Bayesian}} and Optimization Perspective},
  shorttitle = {Machine Learning},
	author = {Theodoridis, Sergios},
  year = {2020},
  edition = {2nd edition},
  publisher = {Elsevier, Academic Press},
  address = {London},
  langid = {english},
  keywords = {Basics,Bayesian,Bayesian Network,Classification,Gaussian processes,Machine learning,MCMC,Monte Carlo,Particle Filter,Probabilistic Machine Learning,Regression,Sampling},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Theodoridis-Machine_learning_2020.pdf}
}

@article{tian2022,
  title = {Real-Time Model Calibration with Deep Reinforcement Learning},
	author = {Tian, Yuan and Chao, Manuel Arias and Kulkarni, Chetan and Goebel, Kai and Fink, Olga},
  year = {2022},
  journal = {Mechanical Systems and Signal Processing},
  volume = {165},
  pages = {108284},
  urldate = {2023-05-10},
  abstract = {The real-time, and accurate inference of model parameters is of great importance in many scientific and engineering disciplines that use computational models (such as a digital twin) for the analysis and prediction of complex physical processes. However, fast and accurate inference for processes of complex systems cannot easily be achieved in real-time with state-of-the-art methods under noisy real-world conditions with the requirement of a real-time response. The primary reason is that the inference of model parameters with traditional techniques based on optimization or sampling often suffers from computational and statistical challenges, resulting in a trade-off between accuracy and deployment time. In this paper, we propose a novel framework for inference of model parameters based on reinforcement learning. The proposed methodology is demonstrated and evaluated on two different physics-based models of turbofan engines. The experimental results demonstrate that the proposed methodology outperforms all other tested methods in terms of speed and robustness, with high inference accuracy.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\NBDESBDI\Tian et al. - 2022 - Real-time model calibration with deep reinforcemen.pdf}
}

@article{tibshirani1996,
  title = {Regression {{Shrinkage}} and {{Selection}} via the {{Lasso}}},
	author = {Tibshirani, Robert},
  year = {1996},
  journal = {Journal of the Royal Statistical Society},
  series = {Series {{B}} ({{Methodological}})},
  volume = {58},
  number = {1},
  pages = {267--288},
  abstract = {We propose a new method for estimation in linear models. The `lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.}
}

@misc{tim2021,
  title = {Scikit-Optimize/Scikit-Optimize},
	author = {Tim, Head and Manoj, Kumar and Holger, Nahrstaedt and Gilles, Louppe and Iaroslav, Shcherbatyi},
  year = {2021},
  urldate = {2022-02-14},
  abstract = {Scikit-Optimize, or skopt, is a simple and efficient library to minimize (very) expensive and noisy black-box functions. It implements several methods for sequential model-based optimization. skopt aims to be accessible and easy to use in many contexts.},
  copyright = {BSD 3-Clause "New" or "Revised" License, Open Access},
  howpublished = {Zenodo},
  keywords = {bayesian-optimization,bayesopt,hyperparameter,machine-learning,optimization,python,scientific-computing}
}

@inproceedings{titsias2009,
  title = {Variational {{Learning}} of {{Inducing Variables}} in {{Sparse Gaussian Processes}}},
  booktitle = {Proceedings of the {{Twelth International Conference}} on {{Artificial Intelligence}} and {{Statistics}}},
	author = {Titsias, Michalis},
  year = {2009},
  pages = {567--574},
  publisher = {PMLR},
  urldate = {2023-06-12},
  abstract = {Sparse Gaussian process methods that use inducing variables require the selection of the inducing inputs and the kernel hyperparameters. We introduce a variational formulation for sparse approximations that jointly infers the inducing inputs and the kernel hyperparameters by maximizing a lower bound of the true log marginal likelihood. The key property of this formulation is that the inducing inputs  are defined to be variational parameters  which are selected by minimizing  the Kullback-Leibler divergence between  the variational distribution and the exact posterior distribution over the latent function values. We apply this technique to regression and we compare it with other approaches in the literature.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Titsias-Variational_Learning_of_Inducing_Variables_in_Sparse_Gaussian_Processes_2009.pdf}
}

@inproceedings{titsias2010,
  title = {Bayesian Gaussian Process Latent Variable Model},
  booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics},
	author = {Titsias, Michalis and Lawrence, Neil D.},
  year = {2010-05-13/2010-05-15},
  series = {Proceedings of Machine Learning Research},
  volume = {9},
  pages = {844--851},
  publisher = {PMLR},
  address = {Chia Laguna Resort, Sardinia, Italy},
  abstract = {We introduce a variational inference framework for training the Gaussian process latent variable model and thus performing Bayesian nonlinear dimensionality reduction. This method allows us to variationally integrate out the input variables of the Gaussian process and compute a lower bound on the exact marginal likelihood of the nonlinear latent variable model. The maximization of the variational lower bound provides a Bayesian training procedure that is robust to overfitting and can automatically select the dimensionality of the nonlinear latent space. We demonstrate our method on real world datasets. The focus in this paper is on dimensionality reduction problems, but the methodology is more general. For example, our algorithm is immediately applicable for training Gaussian process models in the presence of missing or uncertain inputs.}
}

@article{titterington2004,
  title = {Bayesian {{Methods}} for {{Neural Networks}} and {{Related Models}}},
	author = {Titterington, D. M.},
  year = {2004},
  journal = {Statistical Science},
  volume = {19},
  number = {1},
  urldate = {2022-01-21},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Bayesian Neural Networks\Titterington-Bayesian_Methods_for_Neural_Networks_and_Related_Models_2004.pdf}
}

@article{tohme2020,
  title = {A Generalized {{Bayesian}} Approach to Model Calibration},
	author = {Tohme, Tony and Vanslette, Kevin and {Youcef-Toumi}, Kamal},
  year = {2020},
  journal = {Reliability Engineering \& System Safety},
  volume = {204},
  pages = {107141},
  urldate = {2023-02-06},
  abstract = {In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by inverting the validation mathematics into a generalized Bayesian method for model calibration and regression. We perform Bayesian regression based on a user's definition of model-data agreement. This allows for model selection on any type of data distribution, unlike Bayesian and standard regression techniques, that ``fail'' in some cases. We show that our tool is capable of representing and combining least squares, likelihood-based, and Bayesian calibration techniques in a single framework while being able to generalize aspects of these methods. This tool also offers new insights into the interpretation of the predictive envelopes (also known as confidence bands) while giving the analyst more control over these envelopes. We demonstrate the validity of our method by providing three numerical examples to calibrate different models, including a model for energy dissipation in lap joints under impact loading. By calibrating models with respect to the validation metrics one desires a model to ultimately pass, reliability and safety metrics may be integrated into and automatically adopted by the model in the calibration phase.},
  langid = {english},
  keywords = {Bayesian Model Testing,Bayesian Probability Theory,Bayesian Validation Metric,Calibration and Validation,Inference,Regression,Reliability and Safety},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Validation\\Validation Metrics\\Tohme_et_al-A_generalized_Bayesian_approach_to_model_calibration_2020.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\B9R7QZG8\\S0951832020306426.html}
}

@article{tohme2020a,
  title = {A Generalized {{Bayesian}} Approach to Model Calibration},
	author = {Tohme, Tony and Vanslette, Kevin and {Youcef-Toumi}, Kamal},
  year = {2020},
  journal = {Reliability Engineering \& System Safety},
  volume = {204},
  pages = {107141},
  urldate = {2023-05-10},
  abstract = {In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by inverting the validation mathematics into a generalized Bayesian method for model calibration and regression. We perform Bayesian regression based on a user's definition of model-data agreement. This allows for model selection on any type of data distribution, unlike Bayesian and standard regression techniques, that ``fail'' in some cases. We show that our tool is capable of representing and combining least squares, likelihood-based, and Bayesian calibration techniques in a single framework while being able to generalize aspects of these methods. This tool also offers new insights into the interpretation of the predictive envelopes (also known as confidence bands) while giving the analyst more control over these envelopes. We demonstrate the validity of our method by providing three numerical examples to calibrate different models, including a model for energy dissipation in lap joints under impact loading. By calibrating models with respect to the validation metrics one desires a model to ultimately pass, reliability and safety metrics may be integrated into and automatically adopted by the model in the calibration phase.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\SAYBITKW\Tohme et al. - 2020 - A generalized Bayesian approach to model calibrati.pdf}
}

@book{torn1989,
  title = {Global Optimization},
	author = {T{\"o}rn, Aimo and Zhilinskas, A.},
  year = {1989},
  series = {Lecture Notes in Computer Science},
  number = {350},
  publisher = {Springer},
  lccn = {QA402.5 .T685 1989},
  keywords = {Mathematical optimization,Stochastic processes}
}

@article{tsagris2014,
  title = {On the {{Folded Normal Distribution}}},
	author = {Tsagris, Michail and Beneki, Christina and Hassani, Hossein},
  year = {2014},
  journal = {Mathematics},
  volume = {2},
  number = {1},
  pages = {12--28},
  urldate = {2023-12-14},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Tsagris_et_al-On_the_Folded_Normal_Distribution_2014.pdf}
}

@article{tsagris2014a,
  title = {On the {{Folded Normal Distribution}}},
	author = {Tsagris, Michail and Beneki, Christina and Hassani, Hossein},
  year = {2014},
  journal = {Mathematics},
  volume = {2},
  number = {1},
  pages = {12--28},
  urldate = {2024-02-05},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\Tsagris_et_al-On_the_Folded_Normal_Distribution_22.pdf}
}

@article{tuo2021,
  title = {A {{Reproducing Kernel Hilbert Space Approach}} to {{Functional Calibration}} of {{Computer Models}}},
	author = {Tuo, Rui and He, Shiyuan and Pourhabib, Arash and Ding, Yu and Huang, Jianhua Z.},
  year = {2021},
  journal = {Journal of the American Statistical Association},
  volume = {0},
  number = {0},
  pages = {1--15},
  publisher = {Taylor \& Francis},
  urldate = {2023-05-10},
  abstract = {This article develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of functional calibration is motivated by engineering applications where using a constant calibration parameter results in a significant mismatch between outputs from the computer model and the physical experiment. Reproducing kernel Hilbert spaces (RKHS) are used to model the optimal calibration function, defined as the functional relationship between the calibration parameter and control variables that gives the best prediction. This optimal calibration function is estimated through penalized least squares with an RKHS-norm penalty and using physical data. An uncertainty quantification procedure is also developed for such estimates. Theoretical guarantees of the proposed method are provided in terms of prediction consistency and consitency of estimating the optimal calibration function. The proposed method is tested using both real and synthetic data and exhibits more robust performance in prediction and uncertainty quantification than the existing parametric functional calibration method and a state-of-art Bayesian method.},
  keywords = {Calibration,Computer experiment,Reproducing kernel Hilbert spaces,Smoothing splines,Uncertainty quantification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\DBC\KOH\Tuo_et_al-A_Reproducing_Kernel_Hilbert_Space_Approach_to_Functional_Calibration_of_2021.pdf}
}

@article{vanbeek2023,
  title = {Semi-{{Parametric Functional Calibration Using Uncertainty Quantification Based Decision Support}}},
	author = {{van Beek}, Anton and Giuntoli, Andrea and Hansoge, Nitin K. and Keten, Sinan and Chen, Wei},
  year = {2023},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {8},
  number = {021004},
  urldate = {2023-10-18},
  abstract = {While most calibration methods focus on inferring a set of model parameters that are unknown but assumed to be constant, many models have parameters that have a functional relation with the controllable input variables. Formulating a low-dimensional approximation of these calibration functions allows modelers to use low-fidelity models to explore phenomena at lengths and time scales unattainable with their high-fidelity sources. While functional calibration methods are available for low-dimensional problems (e.g., one to three unknown calibration functions), exploring high-dimensional spaces of unknown calibration functions (e.g., more than ten) is still a challenging task due to its computational cost and the risk for identifiability issues. To address this challenge, we introduce a semiparametric calibration method that uses an approximate Bayesian computation scheme to quantify the uncertainty in the unknown calibration functions and uses this insight to identify what functions can be replaced with low-dimensional approximations. Through a test problem and a coarse-grained model of an epoxy resin, we demonstrate that the introduced method enables the identification of a low-dimensional set of calibration functions with a limited compromise in calibration accuracy. The novelty of the presented method is the ability to synthesize domain knowledge from various sources (i.e., physical experiments, simulation models, and expert insight) to enable high-dimensional functional calibration without the need for prior knowledge on the class of unknown calibration functions.},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\van_Beek_et_al-Semi-Parametric_Functional_Calibration_Using_Uncertainty_Quantification_Based_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\7NQF546J\\Semi-Parametric-Functional-Calibration-Using.html}
}

@article{vanderplas2014,
  title = {Frequentism and {{Bayesianism}}: {{A Python-driven Primer}}},
  shorttitle = {Frequentism and {{Bayesianism}}},
	author = {VanderPlas, Jake},
  year = {2014},
  journal = {arXiv:1411.5018},
  eprint = {1411.5018},
  urldate = {2021-09-07},
  abstract = {This paper presents a brief, semi-technical comparison of the essential features of the frequentist and Bayesian approaches to statistical inference, with several illustrative examples implemented in Python. The differences between frequentism and Bayesianism fundamentally stem from differing definitions of probability, a philosophical divide which leads to distinct approaches to the solution of statistical problems as well as contrasting ways of asking and answering questions about unknown parameters. After an example-driven discussion of these differences, we briefly compare several leading Python statistical packages which implement frequentist inference using classical methods and Bayesian inference using Markov Chain Monte Carlo.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Bayesian,Examples,Frequentist},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Statistics\VanderPlas-Frequentism_and_Bayesianism_2014.pdf}
}

@book{vanrossum1995,
  title = {Python Reference Manual},
	author = {Van Rossum, Guido and Drake Jr, Fred L},
  year = {1995},
  publisher = {Centrum voor Wiskunde en Informatica Amsterdam}
}

@misc{vaswani2017,
  title = {Attention {{Is All You Need}}},
	author = {Vaswani, Ashish and Shazeer, Noam and Parmar, Niki and Uszkoreit, Jakob and Jones, Llion and others},
  year = {2017},
  number = {arXiv:1706.03762},
  eprint = {1706.03762},
  primaryclass = {cs},
  publisher = {arXiv},
  urldate = {2023-07-19},
  abstract = {The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Computation and Language,Computer Science - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Vaswani_et_al-Attention_Is_All_You_Need_2017.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\KHP969RB\\1706.html}
}

@incollection{venkateshan2014,
  title = {Numerical {{Integration}}},
  booktitle = {Computational {{Methods}} in {{Engineering}}},
	author = {Venkateshan, S.P. and Swaminathan, Prasanna},
  year = {2014},
  pages = {317--373},
  publisher = {Elsevier},
  urldate = {2022-03-15},
  langid = {english}
}

@article{viana2021,
  title = {A {{Survey}} of {{Bayesian Calibration}} and {{Physics-informed Neural Networks}} in {{Scientific Modeling}}},
	author = {Viana, Felipe A. C. and Subramaniyan, Arun K.},
  year = {2021},
  journal = {Archives of Computational Methods in Engineering},
  volume = {28},
  number = {5},
  pages = {3801--3830},
  urldate = {2021-09-10},
  abstract = {Computer simulations are used to model of complex physical systems. Often, these models represent the solutions (or at least approximations) to partial differential equations that are obtained through costly numerical integration. This paper presents a survey of two important statistical/machine learning approaches that have shaped the field of scientific modeling. Firstly we survey the developments on Bayesian calibration of computer models since the seminal work by Kennedy and O'Hagan. In their paper, the authors proposed an elegant way to use the Gaussian processes to extend calibration beyond parameter and observation uncertainty and include model-form and data size uncertainty. Secondly, we also survey physics-informed neural networks, a topic that has been receiving growing attention due to the potential reduction in computational cost and modeling flexibility. In addition, in order to help the interested reader to familiarize with these topics and venture into custom implementations, we present a summary of applications and software tools. Finally, we close the paper with suggestion for future research directions and a thought provoking call for action.},
  langid = {english},
  keywords = {Model Calibration,Survey},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Viana_Subramaniyan-A_Survey_of_Bayesian_Calibration_and_Physics-informed_Neural_Networks_in_2021.pdf}
}

@article{viana2021a,
  title = {A {{Survey}} of {{Bayesian Calibration}} and {{Physics-informed Neural Networks}} in {{Scientific Modeling}}},
	author = {Viana, Felipe A. C. and Subramaniyan, Arun K.},
  year = {2021},
  journal = {Archives of Computational Methods in Engineering},
  volume = {28},
  number = {5},
  pages = {3801--3830},
  urldate = {2023-02-04},
  abstract = {Computer simulations are used to model of complex physical systems. Often, these models represent the solutions (or at least approximations) to partial differential equations that are obtained through costly numerical integration. This paper presents a survey of two important statistical/machine learning approaches that have shaped the field of scientific modeling. Firstly we survey the developments on Bayesian calibration of computer models since the seminal work by Kennedy and O'Hagan. In their paper, the authors proposed an elegant way to use the Gaussian processes to extend calibration beyond parameter and observation uncertainty and include model-form and data size uncertainty. Secondly, we also survey physics-informed neural networks, a topic that has been receiving growing attention due to the potential reduction in computational cost and modeling flexibility. In addition, in order to help the interested reader to familiarize with these topics and venture into custom implementations, we present a summary of applications and software tools. Finally, we close the paper with suggestion for future research directions and a thought provoking call for action.},
  langid = {english}
}

@article{villemonteix2009,
  title = {Bayesian Optimization for Parameter Identification on a Small Simulation Budget},
	author = {Villemonteix, Julien and Vazquez, Emmanuel and Walter, Eric},
  year = {2009},
  journal = {IFAC Proceedings Volumes},
  volume = {42},
  number = {10},
  pages = {1603--1608},
  urldate = {2021-09-23},
  abstract = {Bayesian optimization uses a probabilistic model of the objective function to guide the search for the optimum. It is particularly interesting for the optimization of expensive-to-evaluate functions. For the last decade, it has been increasingly used for industrial optimization problems and especially for numerical design involving complex computer simulations. We feel that Bayesian optimization should be considered with attention by anyone who has to identify the parameters of a model based on a very limited number of model simulations because of model complexity. In this paper, we wish to describe, as simply as possible, how Bayesian optimization can be used in parameter identification and to present a new application. We concentrate on two algorithms, namely EGO (for Efficient Global Optimization) and IAGO (for Informational Approach to Global Optimization), and describe how they can be used for parameter identification when the budget for evaluating the cost function is severely limited. Some open questions that must be addressed for theoretical and practical reasons are indicated.},
  langid = {english},
  keywords = {Bayesian Optimization,Gaussian processes,Optimization,To Implement},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Design of Experiments\Villemonteix_et_al-Bayesian_optimization_for_parameter_identification_on_a_small_simulation_budget_2009.pdf}
}

@article{virtanen2020,
  title = {{{SciPy}} 1.0: {{Fundamental Algorithms}} for {{Scientific Computing}} in {{Python}}},
	author = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and others},
  year = {2020},
  journal = {Nature Methods},
  volume = {17},
  pages = {261--272},
}

@article{volpp2021,
  title = {{{BAYESIAN CONTEXT AGGREGATION FOR NEURAL PROCESSES}}},
	author = {Volpp, Michael and Fl{\"u}renbrock, Fabian and Grossberger, Lukas and Daniel, Christian and Neumann, Gerhard},
  year = {2021},
  abstract = {Formulating scalable probabilistic regression models with reliable uncertainty estimates has been a long-standing challenge in machine learning research. Recently, casting probabilistic regression as a multi-task learning problem in terms of conditional latent variable (CLV) models such as the Neural Process (NP) has shown promising results. In this paper, we focus on context aggregation, a central component of such architectures, which fuses information from multiple context data points. So far, this aggregation operation has been treated separately from the inference of a latent representation of the target function in CLV models. Our key contribution is to combine these steps into one holistic mechanism by phrasing context aggregation as a Bayesian inference problem. The resulting Bayesian Aggregation (BA) mechanism enables principled handling of task ambiguity, which is key for efficiently processing context information. We demonstrate on a range of challenging experiments that BA consistently improves upon the performance of traditional mean aggregation while remaining computationally efficient and fully compatible with existing NP-based models.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\AP2QWEEW\Volpp et al. - 2021 - BAYESIAN CONTEXT AGGREGATION FOR NEURAL PROCESSES.pdf}
}

@book{vovk2005,
  title = {Algorithmic {{Learning}} in a {{Random World}}},
	author = {Vovk, Vladimir and Gammerman, Alexander and Shafer, Glenn},
  year = {2005},
  publisher = {Springer},
  address = {New York},
  urldate = {2024-01-10},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Conformal Prediction\Algorithmic_Learning_in_a_Random_World_22.pdf}
}

@incollection{voyles,
  title = {Evaluation of {{Model Validation Techniques}} in the {{Presence}} of {{Aleatory}} and {{Epistemic Input Uncertainties}}},
  booktitle = {17th {{AIAA Non-Deterministic Approaches Conference}}},
	author = {Voyles, Ian T. and Roy, Christopher J.},
  publisher = {{American Institute of Aeronautics and Astronautics}},
  urldate = {2023-08-01},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\General\Voyles_Roy-Evaluation_of_Model_Validation_Techniques_in_the_Presence_of_Aleatory_and.pdf}
}

@incollection{voyles2014,
  title = {Evaluation of {{Model Validation Techniques}} in the {{Presence}} of {{Uncertainty}}},
  booktitle = {16th {{AIAA Non-Deterministic Approaches Conference}}},
	author = {Voyles, Ian T. and Roy, Christopher J.},
  year = {2014},
  series = {{{AIAA SciTech Forum}}},
  publisher = {{American Institute of Aeronautics and Astronautics}},
  urldate = {2023-05-24},
  keywords = {American Society of Mechanical Engineers,Compressible Flow,Computational Fluid Dynamics Simulation,Factor of Safety,Freestream Mach Number,Lift Coefficient,Mathematical Models,Probability Distribution Functions,Reynolds Averaged Navier Stokes,Thin Airfoil Theory},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Voyles_Roy-Evaluation_of_Model_Validation_Techniques_in_the_Presence_of_Uncertainty_2014.pdf}
}

@book{waarts2000,
  title = {Structural Reliability Using Finite Element Analysis: An Appraisal of {{DARS}}: Directional Adaptive Response Surface Sampling},
  shorttitle = {Structural Reliability Using Finite Element Analysis},
	author = {Waarts, Paul Hendrik},
  year = {2000},
  publisher = {Delft University Press},
  address = {Delft},
  langid = {english}
}

@misc{wagner2022,
  title = {Kalman {{Bayesian Neural Networks}} for {{Closed-form Online Learning}}},
	author = {Wagner, Philipp and Wu, Xinyang and Huber, Marco F.},
  year = {2022},
  number = {arXiv:2110.00944},
  eprint = {2110.00944},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a BNN, however, is more involved due to the intractability of the underlying Bayesian inference problem and thus, requires efficient approximations. In this paper, we propose a novel approach for BNN learning via closed-form Bayesian inference. For this purpose, the calculation of the predictive distribution of the output and the update of the weight distribution are treated as Bayesian filtering and smoothing problems, where the weights are modeled as Gaussian random variables. This allows closed-form expressions for training the network's parameters in a sequential/online fashion without gradient descent. We demonstrate our method on several UCI datasets and compare it to the state of the art.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Artificial Intelligence,Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Bayesian Neural Networks\\Wagner_et_al-Kalman_Bayesian_Neural_Networks_for_Closed-form_Online_Learning_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\SHSXTQDT\\2110.html}
}

@book{walter1997,
  title = {Identification of Parametric Models from Experimental Data},
	author = {Walter, E. and Pronzato, Luc},
  year = {1997},
  series = {Communications and Control Engineering},
  publisher = {Springer ; Masson},
  address = {Berlin ; New York : Paris},
  langid = {english},
  lccn = {QA402 .W36613 1997},
  keywords = {Parameter estimation,System identification},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Walter_Pronzato-Identification_of_parametric_models_from_experimental_data_1997.pdf}
}

@article{wang2016,
  title = {Bayesian {{Optimization}} in a {{Billion Dimensions}} via {{Random Embeddings}}},
	author = {Wang, Ziyu and Hutter, Frank and Zoghi, Masrour and Matheson, David and {de Freitas}, Nando},
  year = {2016},
  journal = {Journal of Artificial Intelligence Research},
  volume = {55},
  number = {1},
  pages = {361--387},
  urldate = {2023-02-04},
  abstract = {Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesian optimization have identified its scaling to high-dimensions as one of the holy grails of the field. In this paper, we introduce a novel random embedding idea to attack this problem. The resulting Random EMbedding Bayesian Optimization (REMBO) algorithm is very simple, has important invariance properties, and applies to domains with both categorical and continuous variables. We present a thorough theoretical analysis of REMBO. Empirical results confirm that REMBO can effectively solve problems with billions of dimensions, provided the intrinsic dimensionality is low. They also show that REMBO achieves state-of-the-art performance in optimizing the 47 discrete parameters of a popular mixed integer linear programming solver.},
  keywords = {Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Optimization\\BO\\Wang_et_al-Bayesian_Optimization_in_a_Billion_Dimensions_via_Random_Embeddings_2016.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\B8MU2X55\\1301.html}
}

@article{wang2016a,
  title = {Validating {{Dynamic Engineering Models Under Uncertainty}}},
	author = {Wang, Zequn and Fu, Yan and Yang, Ren-Jye and Barbat, Saeed and Chen, Wei},
  year = {2016},
  journal = {Journal of Mechanical Design},
  volume = {138},
  number = {111402},
  urldate = {2023-05-26},
  abstract = {Validating dynamic engineering models is critically important in practical applications by assessing the agreement between simulation results and experimental observations. Though significant progresses have been made, the existing metrics lack the capability of managing uncertainty in both simulations and experiments. In addition, it is challenging to validate a dynamic model aggregately over both the time domain and a model input space with data at multiple validation sites. To overcome these difficulties, this paper presents an area-based metric to systemically handle uncertainty and validate computational models for dynamic systems over an input space by simultaneously integrating the information from multiple validation sites. To manage the complexity associated with a high-dimensional data space, eigenanalysis is performed for the time series data from simulations at each validation site to extract the important features. A truncated Karhunen--Lo{\`e}ve (KL) expansion is then constructed to represent the responses of dynamic systems, resulting in a set of uncorrelated random coefficients with unit variance. With the development of a hierarchical data-fusion strategy, probability integral transform (PIT) is then employed to pool all the resulting random coefficients from multiple validation sites across the input space into a single aggregated metric. The dynamic model is thus validated by calculating the cumulative area difference of the cumulative density functions. The proposed model validation metric for dynamic systems is illustrated with a mathematical example, a supported beam problem with stochastic loads, and real data from the vehicle occupant-restraint system.},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\Wang_et_al-Validating_Dynamic_Engineering_Models_Under_Uncertainty_2016.pdf}
}

@misc{wang2018,
  title = {Controlling {{Sources}} of {{Inaccuracy}} in {{Stochastic Kriging}}},
	author = {Wang, Wenjia and Haaland, Benjamin},
  year = {2018},
  number = {arXiv:1706.00886},
  eprint = {1706.00886},
  primaryclass = {math, stat},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {Scientists and engineers commonly use simulation models to study real systems for which actual experimentation is costly, difficult, or impossible. Many simulations are stochastic in the sense that repeated runs with the same input configuration will result in different outputs. For expensive or time-consuming simulations, stochastic kriging {\textbackslash}citep\{ankenman\} is commonly used to generate predictions for simulation model outputs subject to uncertainty due to both function approximation and stochastic variation. Here, we develop and justify a few guidelines for experimental design, which ensure accuracy of stochastic kriging emulators. We decompose error in stochastic kriging predictions into nominal, numeric, parameter estimation and parameter estimation numeric components and provide means to control each in terms of properties of the underlying experimental design. The design properties implied for each source of error are weakly conflicting and broad principles are proposed. In brief, space-filling properties "small fill distance" and "large separation distance" should balance with replication at distinct input configurations, with number of replications depending on the relative magnitudes of stochastic and process variability. Non-stationarity implies higher input density in more active regions, while regression functions imply a balance with traditional design properties. A few examples are presented to illustrate the results.},
  archiveprefix = {arxiv},
  keywords = {Mathematics - Statistics Theory},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Design of Experiments\\Adaptive Methods\\Wang_Haaland-Controlling_Sources_of_Inaccuracy_in_Stochastic_Kriging_2018.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\LUIYBAVV\\1706.html}
}

@article{wang2019,
  title = {Exact {{Gaussian Processes}} on a {{Million Data Points}}},
	author = {Wang, Ke Alexander and Pleiss, Geoff and Gardner, Jacob R. and Tyree, Stephen and Weinberger, Kilian Q. and others},
  year = {2019},
  urldate = {2023-01-27},
  abstract = {Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about ten thousand training points, necessitating approximations for larger datasets. In this paper, we develop a scalable approach for exact GPs that leverages multi-GPU parallelization and methods like linear conjugate gradients, accessing the kernel matrix only through matrix multiplication. By partitioning and distributing kernel matrix multiplies, we demonstrate that an exact GP can be trained on over a million points, a task previously thought to be impossible with current computing hardware, in less than 2 hours. Moreover, our approach is generally applicable, without constraints to grid data or specific kernel classes. Enabled by this scalability, we perform the first-ever comparison of exact GPs against scalable GP approximations on datasets with \$10{\textasciicircum}4 {\textbackslash}!-{\textbackslash}! 10{\textasciicircum}6\$ data points, showing dramatic performance improvements.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Gaussian Process\Wang_et_al-Exact_Gaussian_Processes_on_a_Million_Data_Points_2019.pdf}
}

@misc{wang2019a,
  title = {Exact {{Gaussian Processes}} on a {{Million Data Points}}},
	author = {Wang, Ke Alexander and Pleiss, Geoff and Gardner, Jacob R. and Tyree, Stephen and Weinberger, Kilian Q. and others},
  year = {2019},
  number = {arXiv:1903.08114},
  eprint = {1903.08114},
  primaryclass = {cs, stat},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about ten thousand training points, necessitating approximations for larger datasets. In this paper, we develop a scalable approach for exact GPs that leverages multi-GPU parallelization and methods like linear conjugate gradients, accessing the kernel matrix only through matrix multiplication. By partitioning and distributing kernel matrix multiplies, we demonstrate that an exact GP can be trained on over a million points, a task previously thought to be impossible with current computing hardware, in less than 2 hours. Moreover, our approach is generally applicable, without constraints to grid data or specific kernel classes. Enabled by this scalability, we perform the first-ever comparison of exact GPs against scalable GP approximations on datasets with \$10{\textasciicircum}4 {\textbackslash}!-{\textbackslash}! 10{\textasciicircum}6\$ data points, showing dramatic performance improvements.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Distributed Parallel and Cluster Computing,Computer Science - Machine Learning,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Wang_et_al-Exact_Gaussian_Processes_on_a_Million_Data_Points_22.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\8S5M93PJ\\1903.html}
}

@article{wang2019b,
  title = {{{ESC}}: An Efficient Error-Based Stopping Criterion for Kriging-Based Reliability Analysis Methods},
  shorttitle = {{{ESC}}},
	author = {Wang, Zeyu and Shafieezadeh, Abdollah},
  year = {2019},
  journal = {Structural and Multidisciplinary Optimization},
  volume = {59},
  number = {5},
  pages = {1621--1637},
  urldate = {2024-02-09},
  abstract = {The ever-increasing complexity of numerical models and associated computational demands have challenged classical reliability analysis methods. Surrogate model-based reliability analysis techniques, and in particular those using kriging meta-model, have gained considerable attention recently for their ability to achieve high accuracy and computational efficiency. However, existing stopping criteria, which are used to terminate the training of surrogate models, do not directly relate to the error in estimated failure probabilities. This limitation can lead to high computational demands because of unnecessary calls to costly performance functions (e.g., involving finite element models) or potentially inaccurate estimates of failure probability due to premature termination of the training process. Here, we propose the error-based stopping criterion (ESC) to address these limitations. First, it is shown that the total number of wrong sign estimation of the performance function for candidate design samples by kriging, S, follows a Poisson binomial distribution. This finding is subsequently used to estimate the lower and upper bounds of S for a given confidence level for sets of candidate design samples classified by kriging as safe and unsafe. An upper bound of error of the estimated failure probability is subsequently derived according to the probabilistic properties of Poisson binomial distribution. The proposed upper bound is implemented in the kriging-based reliability analysis method as the stopping criterion. The efficiency and robustness of ESC are investigated here using five benchmark reliability analysis problems. Results indicate that the proposed method achieves the set accuracy target and substantially reduces the computational demand, in some cases by over 50\%.},
  langid = {english},
  keywords = {Adaptive kriging,Estimation error,Poisson binomial distribution,Reliability analysis,Stopping criterion,Surrogate model}
}

@article{wang2020,
  title = {A {{Survey}} on {{Bayesian Deep Learning}}},
	author = {Wang, Hao and Yeung, Dit-Yan},
  year = {2020},
  journal = {ACM Computing Surveys},
  volume = {53},
  number = {5},
  pages = {1--37},
  urldate = {2022-01-21},
  abstract = {A comprehensive artificial intelligence system needs to not only perceive the environment with different ``senses'' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty. The past decade has seen major advances in many perception tasks, such as visual object recognition and speech recognition, using deep learning models. For higher-level inference, however, probabilistic graphical models with their Bayesian nature are still more powerful and flexible. In recent years,               Bayesian deep learning               has emerged as a unified probabilistic framework to tightly integrate deep learning and Bayesian models.               1               In this general framework, the perception of text or images using deep learning can boost the performance of higher-level inference and, in turn, the feedback from the inference process is able to enhance the perception of text or images. This survey provides a comprehensive introduction to               Bayesian deep learning               and reviews its recent applications on recommender systems, topic models, control, and so on. We also discuss the relationship and differences between Bayesian deep learning and other related topics, such as Bayesian treatment of neural networks.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Machine Learning\Bayesian Neural Networks\Wang_Yeung-A_Survey_on_Bayesian_Deep_Learning_2020.pdf}
}

@article{wang2020a,
  title = {Statistical Analysis of Accelerated Temperature Cycling Test Based on {{Coffin-Manson}} Model},
	author = {Wang, Yudong and Tang, Yincai},
  year = {2020},
  journal = {Communications in Statistics - Theory and Methods},
  volume = {49},
  number = {15},
  pages = {3663--3680},
  publisher = {Taylor \& Francis},
  urldate = {2023-05-30},
  abstract = {This paper investigates the statistical analysis of grouped accelerated temperature cycling test data when the product lifetime follows a Weibull distribution. A log-linear acceleration equation is derived from the Coffin-Manson model. The problem is transformed to a constant-stress accelerated life test with grouped data and multiple acceleration variables. The Jeffreys prior and reference priors are derived. Maximum likelihood estimation and Bayesian estimation with objective priors are obtained by applying the technique of data augmentation. A simulation study shows that both of these two methods perform well when sample size is large, and the Bayesian method gives better performance under small sample sizes.},
  keywords = {Coffin-Manson model,data augmentation,grouped data,objective prior},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Lifetime Coffin Manson\Statistical_analysis_of_accelerated_temperature_cycling_test_based_on.pdf}
}

@article{wang2023,
  title = {Recent {{Advances}} in {{Bayesian Optimization}}},
	author = {Wang, Xilu and Jin, Yaochu and Schmitt, Sebastian and Olhofer, Markus},
  year = {2023},
  journal = {ACM Computing Surveys},
  urldate = {2023-06-05},
  abstract = {Bayesian optimization has emerged at the forefront of expensive black-box optimization due to its data efficiency. Recent years have witnessed a proliferation of studies on the development of new Bayesian optimization algorithms and their applications. Hence, this paper attempts to provide a comprehensive and updated survey of recent advances in Bayesian optimization that are mainly based on Gaussian processes and identify challenging open problems. We categorize the existing work on Bayesian optimization into nine main groups according to the motivations and focus of the proposed algorithms. For each category, we present the main advances with respect to the construction of surrogate models and adaptation of the acquisition functions. Finally, we discuss the open questions and suggest promising future research directions, in particular with regard to heterogeneity, privacy preservation, and fairness in distributed and federated optimization systems.},
  keywords = {acquisition function,Bayesian optimization,Gaussian process},
  annotation = {Just Accepted},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Optimization\BO\Wang_et_al-Recent_Advances_in_Bayesian_Optimization_2023.pdf}
}

@article{wang2023a,
  title = {Quantification and Propagation of {{Aleatoric}} Uncertainties in Topological Structures},
	author = {Wang, Zihan and Daeipour, Mohamad and Xu, Hongyi},
  year = {2023},
  journal = {Reliability Engineering \& System Safety},
  volume = {233},
  pages = {109122},
  urldate = {2023-07-19},
  abstract = {Quantification and propagation of aleatoric uncertainties distributed in complex topological structures remain a challenge. Existing uncertainty quantification and propagation approaches can only handle parametric uncertainties or high dimensional random quantities distributed in a simply connected spatial domain. There lacks a systematic method that captures the topological characteristics of the structural domain in uncertainty analysis. Therefore, this paper presents a new methodology that quantifies and propagates aleatoric uncertainties, such as the spatially varying local material properties and defects, distributed in a topological spatial domain. We propose a new random field-based uncertainty representation approach that captures the topological characteristics using the shortest interior path distance. Parameterization methods like PPCA and {$\beta$}-Variational Autoencoder ({$\beta$}VAE) are employed to convert the random field representation of uncertainty to a small set of independent random variables. Then non-intrusive uncertainties propagation methods such as polynomial chaos expansion and univariate dimension reduction are employed to propagate the parametric uncertainties to the output of the problem. The effectiveness of the proposed methodology is demonstrated by engineering case studies. The accuracy and computational efficiency of the proposed method is confirmed by comparing with the reference values of Monte Carlo simulations with a sufficiently large number of samples.},
  langid = {english},
  keywords = {Aleatoric uncertainty,Non-simply connected space,Random field,Topological structure,Uncertainty propagation,Uncertainty quantification},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\GI9DXDCV\S0951832023000376.html}
}

@article{wang2023b,
  title = {A New Active-Learning Estimation Method for the Failure Probability of Structural Reliability Based on {{Kriging}} Model and Simple Penalty Function},
	author = {Wang, Yanjin and Pan, Hao and Shi, Yina and Wang, Ruili and Wang, Pei},
  year = {2023},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {410},
  pages = {116035},
  urldate = {2023-12-01},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Reliability Analysis\Wang_et_al-A_new_active-learning_estimation_method_for_the_failure_probability_of_2023.pdf}
}

@misc{wenger2022,
  title = {Posterior and {{Computational Uncertainty}} in {{Gaussian Processes}}},
	author = {Wenger, Jonathan and Pleiss, Geoff and Pf{\"o}rtner, Marvin and Hennig, Philipp and Cunningham, John P.},
  year = {2022},
  number = {arXiv:2205.15449},
  eprint = {2205.15449},
  primaryclass = {cs, math, stat},
  publisher = {arXiv},
  urldate = {2023-02-04},
  abstract = {Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited computation, is entirely ignored when using the approximate posterior. Therefore in practice, GP models are often as much about the approximation method as they are about the data. Here, we develop a new class of methods that provides consistent estimation of the combined uncertainty arising from both the finite number of data observed and the finite amount of computation expended. The most common GP approximations map to an instance in this class, such as methods based on the Cholesky factorization, conjugate gradients, and inducing points. For any method in this class, we prove (i) convergence of its posterior mean in the associated RKHS, (ii) decomposability of its combined posterior covariance into mathematical and computational covariances, and (iii) that the combined variance is a tight worst-case bound for the squared error between the method's posterior mean and the latent function. Finally, we empirically demonstrate the consequences of ignoring computational uncertainty and show how implicitly modeling it improves generalization performance on benchmark datasets.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Mathematics - Numerical Analysis,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Machine Learning\\Gaussian Process\\Wenger_et_al-Posterior_and_Computational_Uncertainty_in_Gaussian_Processes_2022.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\6M7XNZHE\\2205.html}
}

@article{white2022,
  title = {Multi-{{Metric Validation Under Uncertainty}} for {{Multivariate Model Outputs}} and {{Limited Measurements}}},
	author = {White, Andrew and Mahadevan, Sankaran and Schmucker, Jason and Karl, Alexander},
  year = {2022},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {7},
  number = {4},
  pages = {041004},
  urldate = {2023-09-22},
  abstract = {Abstract             Model validation for real-world systems involves multiple sources of uncertainty, multivariate model outputs, and often a limited number of measurement samples. These factors preclude the use of many existing validation metrics, or at least limit the ability of the practitioner to derive insights from computed metrics. This paper seeks to extend the area metric (univariate only) and the model reliability metric (univariate and multivariate) to account for these issues. The model reliability metric was found to be more extendable to multivariate outputs, whereas the area metric presented some difficulties. Metrics of different types (area and model reliability), dimensionality (univariate and multivariate), and objective (bias effects, shape effects, or both) are used together in a ``multimetric'' approach that provides a more informative validation assessment. The univariate metrics can be used for output-by-output model diagnosis and the multivariate metrics contributes an overall model assessment that includes correlation among the outputs. The extensions to the validation metrics in this paper address limited measurement sample size, improve the interpretability of the metric results by separating the effects of distribution bias and shape, and enhance the model reliability metric's tolerance parameter. The proposed validation approach is demonstrated with a bivariate numerical example and then applied to a gas turbine engine heat transfer model.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Validation\Validation Metrics\White_et_al-Multi-Metric_Validation_Under_Uncertainty_for_Multivariate_Model_Outputs_and_2022.pdf}
}

@article{white2023,
  title = {Multi-{{Metric Validation Under Uncertainty}} for {{Multivariate Model Outputs}} and {{Limited Measurements}}},
	author = {White, Andrew and Mahadevan, Sankaran and Schmucker, Jason and Karl, Alexander},
  year = {2023},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {7},
  number = {4},
  urldate = {2023-02-04},
  abstract = {Model validation for real-world systems involves multiple sources of uncertainty, multivariate model outputs, and often a limited number of measurement samples. These factors preclude the use of many existing validation metrics, or at least limit the ability of the practitioner to derive insights from computed metrics. This paper seeks to extend the area metric (univariate only) and the model reliability metric (univariate and multivariate) to account for these issues. The model reliability metric was found to be more extendable to multivariate outputs, whereas the area metric presented some difficulties. Metrics of different types (area and model reliability), dimensionality (univariate and multivariate), and objective (bias effects, shape effects, or both) are used together in a ``multimetric'' approach that provides a more informative validation assessment. The univariate metrics can be used for output-by-output model diagnosis and the multivariate metrics contributes an overall model assessment that includes correlation among the outputs. The extensions to the validation metrics in this paper address limited measurement sample size, improve the interpretability of the metric results by separating the effects of distribution bias and shape, and enhance the model reliability metric's tolerance parameter. The proposed validation approach is demonstrated with a bivariate numerical example and then applied to a gas turbine engine heat transfer model.},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\A84F8AID\Multi-Metric-Validation-Under-Uncertainty-for.html}
}

@article{white2023a,
  title = {Discrepancy Modeling for Model Calibration with Multivariate Output},
	author = {White, Andrew and Mahadevan, Sankaran},
  year = {2023},
  journal = {International Journal for Uncertainty Quantification},
  volume = {13},
  number = {6},
  publisher = {Begel House Inc.},
  urldate = {2023-05-13},
  abstract = {This paper explores the application of the Kennedy and O'Hagan (KOH) Bayesian framework to the calibration of physics models with multivariate outputs by formul...},
  langid = {english}
}

@article{whiting2023,
  title = {Assessment of {{Model Validation}}, {{Calibration}}, and {{Prediction Approaches}} in the {{Presence}} of {{Uncertainty}}},
	author = {Whiting, Nolan W. and Roy, Christopher J. and Duque, Earl and Lawrence, Seth and Oberkampf, William L.},
  year = {2023},
  journal = {Journal of Verification, Validation and Uncertainty Quantification},
  volume = {8},
  number = {1},
  pages = {011001},
  urldate = {2023-09-22},
  abstract = {Abstract             Model validation is the process of determining the degree to which a model is an accurate representation of the true value in the real world. The results of a model validation study can be used to either quantify the model form uncertainty or to improve/calibrate the model. The model validation process becomes complex when there is uncertainty in the simulation and/or experimental outcomes. These uncertainties can be in the form of aleatory uncertainties due to randomness or epistemic uncertainties due to lack of knowledge. Five different approaches are used for addressing model validation and predictive capability: (1) the area validation metric (AVM), (2) a modified area validation metric (MAVM) with confidence intervals, (3) the validation uncertainty procedure from ASME V\&V 20, (4) a calibration procedure interpreted from ASME V\&V 20, and (5) identification of the model discrepancy term using Bayesian estimation. To provide an unambiguous assessment of these different approaches, synthetic experimental data is generated from computational fluid dynamics simulations of an airfoil with a flap. A simplified model is then developed using thin airfoil theory. The accuracy of the simplified model is assessed using the synthetic experimental data. The quantities examined include the two-dimensional lift and moment coefficients for the airfoil with varying angles of attack and flap deflection angles. Each of these approaches is assessed for the ability to tightly encapsulate the true value at conditions both where experimental results are provided and prediction locations where no experimental data are available. Generally, it was seen that the MAVM performed the best in cases where there is a sparse amount of data and/or large extrapolations. Furthermore, it was found that Bayesian estimation outperformed the others where there is an extensive amount of experimental data that covers the application domain.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\M3VIV9AR\vvuq_008_01_011001.pdf}
}

@misc{wilson2017,
  title = {The Reparameterization Trick for Acquisition Functions},
	author = {Wilson, James T. and Moriconi, Riccardo and Hutter, Frank and Deisenroth, Marc Peter},
  year = {2017},
  number = {arXiv:1712.00424},
  eprint = {1712.00424},
  primaryclass = {cs, math, stat},
  publisher = {arXiv},
  urldate = {2023-05-18},
  abstract = {Bayesian optimization is a sample-efficient approach to solving global optimization problems. Along with a surrogate model, this approach relies on theoretically motivated value heuristics (acquisition functions) to guide the search process. Maximizing acquisition functions yields the best performance; unfortunately, this ideal is difficult to achieve since optimizing acquisition functions per se is frequently non-trivial. This statement is especially true in the parallel setting, where acquisition functions are routinely non-convex, high-dimensional, and intractable. Here, we demonstrate how many popular acquisition functions can be formulated as Gaussian integrals amenable to the reparameterization trick and, ensuingly, gradient-based optimization. Further, we use this reparameterized representation to derive an efficient Monte Carlo estimator for the upper confidence bound acquisition function in the context of parallel selection.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Machine Learning,Mathematics - Optimization and Control,Statistics - Machine Learning},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Optimization\\BO\\Wilson_et_al-The_reparameterization_trick_for_acquisition_functions_2017.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\YVPRRDI4\\1712.html}
}

@article{wu,
  title = {Disentangled {{Multi-Fidelity Deep Bayesian Active Learning}}},
	author = {Wu, Dongxia and Niu, Ruijia and Chinazzi, Matteo and Ma, Yi-An and Yu, Rose},
  abstract = {To balance quality and cost, various domain areas of science and engineering run simulations at multiple levels of sophistication. Multi-fidelity active learning aims to learn a direct mapping from input parameters to simulation outputs at the highest fidelity by actively acquiring data from multiple fidelity levels. However, existing approaches based on Gaussian processes are hardly scalable to high-dimensional data. Deep learning-based methods often impose a hierarchical structure in hidden representations, which only supports passing information from low-fidelity to high-fidelity. These approaches can lead to the undesirable propagation of errors from lowfidelity representations to high-fidelity ones. We propose a novel framework called Disentangled Multi-fidelity Deep Bayesian Active Learning (D-MFDAL), which learns the surrogate models conditioned on the distribution of functions at multiple fidelities. On benchmark tasks of learning deep surrogates of partial differential equations including heat equation, Poisson's equation and fluid simulations, our approach significantly outperforms state-of-the-art in prediction accuracy and sample efficiency.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\VIAP4ZII\Wu et al. - Disentangled Multi-Fidelity Deep Bayesian Active L.pdf}
}

@article{wu2018,
  title = {Inverse Uncertainty Quantification Using the Modular {{Bayesian}} Approach Based on {{Gaussian}} Process, {{Part}} 1: {{Theory}}},
  shorttitle = {Inverse Uncertainty Quantification Using the Modular {{Bayesian}} Approach Based on {{Gaussian}} Process, {{Part}} 1},
	author = {Wu, Xu and Kozlowski, Tomasz and Meidani, Hadi and Shirvan, Koroush},
  year = {2018},
  journal = {Nuclear Engineering and Design},
  volume = {335},
  pages = {339--355},
  urldate = {2023-02-04},
  abstract = {In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. ``Expert opinion'' and ``user self-evaluation'' have been widely used to specify computer model input uncertainties in previous uncertainty, sensitivity and validation studies. Inverse Uncertainty Quantification (UQ) is the process to inversely quantify input uncertainties based on experimental data in order to more precisely quantify such ad-hoc specifications of the input uncertainty information. In this paper, we used Bayesian analysis to establish the inverse UQ formulation, with systematic and rigorously derived metamodels constructed by Gaussian Process (GP). Due to incomplete or inaccurate underlying physics, as well as numerical approximation errors, computer models always have discrepancy/bias in representing the realities, which can cause over-fitting if neglected in the inverse UQ process. The model discrepancy term is accounted for in our formulation through the ``model updating equation''. We provided a detailed introduction and comparison of the full and modular Bayesian approaches for inverse UQ, as well as pointed out their limitations when extrapolated to the validation/prediction domain. Finally, we proposed an improved modular Bayesian approach that can avoid extrapolating the model discrepancy that is learnt from the inverse UQ domain to the validation/prediction domain.},
  langid = {english},
  keywords = {Bayesian calibration,Gaussian process,Inverse uncertainty quantification,Model discrepancy,Modular Bayesian},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\Wu_et_al-Inverse_uncertainty_quantification_using_the_modular_Bayesian_approach_based_on_2018.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\J3FWLVRB\\S0029549318306423.html}
}

@article{wu2023,
  title = {A Comprehensive Study of Non-Adaptive and Residual-Based Adaptive Sampling for Physics-Informed Neural Networks},
	author = {Wu, Chenxi and Zhu, Min and Tan, Qinyang and Kartha, Yadhu and Lu, Lu},
  year = {2023},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {403},
  pages = {115671},
  urldate = {2023-06-12},
  abstract = {Physics-informed neural networks (PINNs) have shown to be effective tools for solving both forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network using automatic differentiation, and this PDE loss is evaluated at a set of scattered spatio-temporal points (called residual points). The location and distribution of these residual points are highly important to the performance of PINNs. However, in the existing studies on PINNs, only a few simple residual point sampling methods have mainly been used. Here, we present a comprehensive study of two categories of sampling for PINNs: non-adaptive uniform sampling and adaptive nonuniform sampling. We consider six uniform sampling methods, including (1) equispaced uniform grid, (2) uniformly random sampling, (3) Latin hypercube sampling, (4) Halton sequence, (5) Hammersley sequence, and (6) Sobol sequence. We also consider a resampling strategy for uniform sampling. To improve the sampling efficiency and the accuracy of PINNs, we propose two new residual-based adaptive sampling methods: residual-based adaptive distribution (RAD) and residual-based adaptive refinement with distribution (RAR-D), which dynamically improve the distribution of residual points based on the PDE residuals during training. Hence, we have considered a total of 10 different sampling methods, including six non-adaptive uniform sampling, uniform sampling with resampling, two proposed adaptive sampling, and an existing adaptive sampling. We extensively tested the performance of these sampling methods for four forward problems and two inverse problems in many setups. Our numerical results presented in this study are summarized from more than 6000 simulations of PINNs. We show that the proposed adaptive sampling methods of RAD and RAR-D significantly improve the accuracy of PINNs with fewer residual points for both forward and inverse problems. The results obtained in this study can also be used as a practical guideline in choosing sampling methods.},
  langid = {english},
  keywords = {Non-adaptive uniform sampling,Partial differential equations,Physics-informed neural networks,Residual point distribution,Residual-based adaptive sampling,Uniform sampling with resampling},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Design of Experiments\\Adaptive Methods\\Wu_et_al-A_comprehensive_study_of_non-adaptive_and_residual-based_adaptive_sampling_for_2023.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\BXAEDQBV\\S0045782522006260.html}
}

@article{xiong2009,
  title = {A Better Understanding of Model Updating Strategies in Validating Engineering Models},
	author = {Xiong, Ying and Chen, Wei and Tsui, Kwok-Leung and Apley, Daniel W.},
  year = {2009},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {198},
  number = {15-16},
  pages = {1327--1337},
  urldate = {2023-05-10},
  abstract = {Our objective in this work is to provide a better understanding of the various model updating strategies that utilize mathematical means to update a computer model based on both physical and computer observations. We examine different model updating formulations, e.g. calibration and bias-correction, as well as different solution methods. Traditional approaches to calibration treat certain computer model parameters as fixed over the physical experiment, but unknown, and the objective is to infer values for the so-called calibration parameters that provide a better match between the physical and computer data. In many practical applications, however, certain computer model parameters vary from trial to trial over the physical experiment, in which case there is no single calibrated value for a parameter. We pay particular attention to this situation and develop a maximum likelihood estimation (MLE) approach for estimating the distributional properties of the randomly varying parameters which, in a sense, calibrates them to provide the best agreement between physical and computer observations. Furthermore, we employ the newly developed u-pooling method (by Ferson et al.) as a validation metric to assess the accuracy of an updated model over a region of interest. Using the benchmark thermal challenge problem as an example, we study several possible model updating formulations using the proposed methodology. The effectiveness of the various formulations is examined. The benefits and limitations of using the MLE method versus a Bayesian approach are presented. Our study also provides insights into the potential benefits and limitations of using model updating for improving the predictive capability of a model.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\383E563F\Xiong et al. - 2009 - A better understanding of model updating strategie.pdf}
}

@article{xiong2009a,
  title = {A Better Understanding of Model Updating Strategies in Validating Engineering Models},
	author = {Xiong, Ying and Chen, Wei and Tsui, Kwok-Leung and Apley, Daniel W.},
  year = {2009},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {198},
  number = {15},
  pages = {1327--1337},
  urldate = {2023-10-16},
  abstract = {Our objective in this work is to provide a better understanding of the various model updating strategies that utilize mathematical means to update a computer model based on both physical and computer observations. We examine different model updating formulations, e.g. calibration and bias-correction, as well as different solution methods. Traditional approaches to calibration treat certain computer model parameters as fixed over the physical experiment, but unknown, and the objective is to infer values for the so-called calibration parameters that provide a better match between the physical and computer data. In many practical applications, however, certain computer model parameters vary from trial to trial over the physical experiment, in which case there is no single calibrated value for a parameter. We pay particular attention to this situation and develop a maximum likelihood estimation (MLE) approach for estimating the distributional properties of the randomly varying parameters which, in a sense, calibrates them to provide the best agreement between physical and computer observations. Furthermore, we employ the newly developed u-pooling method (by Ferson et al.) as a validation metric to assess the accuracy of an updated model over a region of interest. Using the benchmark thermal challenge problem as an example, we study several possible model updating formulations using the proposed methodology. The effectiveness of the various formulations is examined. The benefits and limitations of using the MLE method versus a Bayesian approach are presented. Our study also provides insights into the potential benefits and limitations of using model updating for improving the predictive capability of a model.},
  keywords = {Bayesian approach,Maximum likelihood estimation,Model updating,Model validation,Thermal challenge problem},
  file = {C\:\\Users\\sven1\\SynologyDrive\\Arbeiten_Uni\\Promotion\\03 - Literatur\\Zotero_Literature\\PhD\\Model Calibration\\Xiong_et_al-A_better_understanding_of_model_updating_strategies_in_validating_engineering_2009.pdf;C\:\\Users\\sven1\\Documents\\Zotero_database\\storage\\GNGJZ6JS\\S0045782508004258.html}
}

@article{yang2018,
  title = {A Benchmark and Comparison of Active Learning for Logistic Regression},
	author = {Yang, Yazhou and Loog, Marco},
  year = {2018},
  journal = {Pattern Recognition},
  volume = {83},
  pages = {401--415},
  abstract = {Logistic regression is by far the most widely used classifier in real-world applications. In this paper, we benchmark the state-of-the-art active learning methods for logistic regression and discuss and illustrate their underlying characteristics. Experiments are carried out on three synthetic datasets and 44 real-world datasets, providing insight into the behaviors of these active learning methods with respect to the area of the learning curve (which plots classification accuracy as a function of the number of queried examples) and their computational costs. Surprisingly, one of the earliest and simplest suggested active learning methods, i.e., uncertainty sampling, performs exceptionally well overall. Another remarkable finding is that random sampling, which is the rudimentary baseline to improve upon, is not overwhelmed by individual active learning techniques in many cases.},
  keywords = {Active learning,Benchmark,Experimental design,Logistic regression,Preference maps}
}

@article{yeo2000,
  title = {A New Family of Power Transformations to Improve Normality or Symmetry},
	author = {Yeo, In-Kwon and Johnson, Richard A.},
  year = {2000},
  journal = {Biometrika},
  volume = {87},
  number = {4},
  eprint = {2673623},
  eprinttype = {jstor},
  pages = {954--959},
  urldate = {2024-02-08},
  abstract = {We introduce a new power transformation family which is well defined on the whole real line and which is appropriate for reducing skewness and to approximate normality. It has properties similar to those of the Box-Cox transformation for positive variables. The large-sample properties of the transformation are investigated in the contect of a single random sample}
}

@article{yuen2002,
  title = {Bayesian {{Modal Updating}} Using {{Complete Input}} and {{Incomplete Response Noisy Measurements}}},
	author = {Yuen, Ka-Veng and Katafygiotis, Lambros S.},
  year = {2002},
  journal = {Journal of Engineering Mechanics},
  volume = {128},
  number = {3},
  pages = {340--350},
  urldate = {2023-05-10},
  abstract = {The problem of identification of the modal parameters of a structural model using complete input and incomplete response time histories is addressed. It is assumed that there exist both input error ͑due to input measurement noise͒ and output error ͑due to output measurement noise and modeling error͒. These errors are modeled by independent white noise processes, and contribute towards uncertainty in the identification of the modal parameters of the model. To explicitly treat these uncertainties, a Bayesian framework is adopted and a Bayesian time-domain methodology for modal updating based on an approximate conditional probability expansion is presented. The methodology allows one to obtain not only the optimal ͑most probable͒ values of the updated modal parameters but also their uncertainties, calculated from their joint probability distribution. Calculation of the uncertainties of the identified modal parameters is very important if one plans to proceed with the updating of a theoretical finite-element model based on these modal estimates. The proposed approach requires only one set of excitation and corresponding response data. It is found that the updated probability density function ͑PDF͒ can be well approximated by a Gaussian distribution centered at the optimal parameters at which the posterior PDF is maximized. Numerical examples using noisy simulated data are presented to illustrate the proposed method.},
  langid = {english},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\W44HFL6D\Yuen and Katafygiotis - 2002 - Bayesian Modal Updating using Complete Input and I.pdf}
}

@article{zang2008,
  title = {Model Validation for Structural Dynamic Analysis: {{An}} Approach to the {{Sandia Structural Dynamics Challenge}}},
  shorttitle = {Model Validation for Structural Dynamic Analysis},
	author = {Zang, C. and Schwingshackl, C.W. and Ewins, D.J.},
  year = {2008},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {197},
  number = {29-32},
  pages = {2645--2659},
  urldate = {2023-09-07},
  langid = {english}
}

@article{ziatdinov2022,
  title = {Physics Makes the Difference: {{Bayesian}} Optimization and Active Learning via Augmented {{Gaussian}} Process},
  shorttitle = {Physics Makes the Difference},
	author = {Ziatdinov, Maxim A. and Ghosh, Ayana and Kalinin, Sergei V.},
  year = {2022},
  journal = {Machine Learning: Science and Technology},
  volume = {3},
  number = {1},
  pages = {015003},
  publisher = {IOP Publishing},
  urldate = {2023-02-04},
  abstract = {Both experimental and computational methods for the exploration of structure, functionality, and properties of materials often necessitate the search across broad parameter spaces to discover optimal experimental conditions and regions of interest in the image space or parameter space of computational models. The direct grid search of the parameter space tends to be extremely time-consuming, leading to the development of strategies balancing exploration of unknown parameter spaces and exploitation towards required performance metrics. However, classical Bayesian optimization (BO) strategies based on the Gaussian process (GP) do not readily allow for the incorporation of the known physical behaviors or past knowledge. Here we explore a hybrid optimization/exploration algorithm created by augmenting the standard GP with a structured probabilistic model of the expected system's behavior. This approach balances the flexibility of the non-parametric GP approach with a rigid structure of physical knowledge encoded into the parametric model. The fully Bayesian treatment of the latter allows additional control over the optimization via the selection of priors for the model parameters. The method is demonstrated for a noisy version of a standard univariate test function used to evaluate optimization algorithms and further extended to physical lattice models. This methodology is expected to be universally suitable for injecting prior knowledge in the form of physical models and past data in the BO framework.},
  langid = {english},
  file = {C:\Users\sven1\SynologyDrive\Arbeiten_Uni\Promotion\03 - Literatur\Zotero_Literature\PhD\Model Calibration\Ziatdinov_et_al-Physics_makes_the_difference_2022.pdf}
}

@misc{zotero-1002,
  title = {Wiley-{{VCH}} - {{Statistical Methods}} for {{Reliability Data}}},
  urldate = {2023-09-08},
  howpublished = {https://www.wiley-vch.de/en/areas-interest/mathematics-statistics/statistics-16st/quality-productivity-reliability-16st8/statistical-methods-for-reliability-data-978-1-118-11545-9},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\9PP4ZB7X\statistical-methods-for-reliability-data-978-1-118-11545-9.html}
}

@misc{zotero-1205,
  title = {{Kleinanzeigen}},
  journal = {Kleinanzeigen},
  urldate = {2024-01-11},
  howpublished = {https://www.kleinanzeigen.de/m-einstellungen.html\#/payment-settings},
  langid = {ngerman},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\W6BWR5RS\m-einstellungen.html}
}

@misc{zotero-1250,
  title = {{{DIN EN}} 61508-1 - 2011-02 - {{Beuth}}.De},
  urldate = {2024-02-02},
  howpublished = {https://www.beuth.de/de/norm/din-en-61508-1/135302584},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\4H9X7FJK\135302584.html}
}

@misc{zotero-1292,
  urldate = {2024-02-21},
  howpublished = {file:///C:/Users/sven1/SynologyDrive/Arbeiten\_Uni/Promotion/03\%20-\%20Literatur/Zotero\_Literature/PhD/Machine\%20Learning/Neural\%20Process/},
  file = {C:\Users\sven1\Documents\Zotero_database\storage\PE5H8JEW\Neural Process.xml}
}

@misc{zotero-781,
  title = {Statistical Analysis of Accelerated Temperature Cycling Test Based on {{Coffin-Manson}} Model: {{Communications}} in {{Statistics}} - {{Theory}} and {{Methods}}: {{Vol}} 49, {{No}} 15},
  urldate = {2023-05-30},
  howpublished = {https://www.tandfonline.com/doi/abs/10.1080/03610926.2019.1702697}
}
