@article{najmUncertaintyQuantificationChemical2009,
	title = {Uncertainty Quantification in Chemical Systems},
	author = {Najm, H. N. and Debusschere, B. J. and Marzouk, Y. M. and Widmer,
	          S. and Le Ma{\^i}tre, O. P.},
	year = {2009},
	journal = {International Journal for Numerical Methods in Engineering},
	volume = {80},
	number = {6-7},
	pages = {789--814},
	issn = {1097-0207},
	doi = {https://doi.org/10.1002/nme.2551},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.2551},
	urldate = {2024-11-01},
	abstract = {We demonstrate the use of multiwavelet spectral polynomial chaos
	            techniques for uncertainty quantification in non-isothermal
	            ignition of a methane--air system. We employ Bayesian inference
	            for identifying the probabilistic representation of the uncertain
	            parameters and propagate this uncertainty through the ignition
	            process. We analyze the time evolution of moments and probability
	            density functions of the solution. We also examine the role and
	            significance of dependence among the uncertain parameters. We
	            finish with a discussion of the role of non-linearity and the
	            performance of the algorithm. Copyright {\copyright} 2009 John
	            Wiley \& Sons, Ltd.},
	copyright = {Copyright {\copyright} 2009 John Wiley \& Sons, Ltd.},
	langid = {english},
	keywords = {chemistry,ignition,multiwavelet,polynomial chaos,uncertainty
	            quantification},
}

@article{grovesBayesianRegressionFacilitates2024,
	title = {Bayesian Regression Facilitates Quantitative Modeling of Cell
	         Metabolism},
	author = {Groves, Teddy and Cowie, Nicholas Luke and Nielsen, Lars Keld},
	year = {2024},
	month = apr,
	journal = {ACS Synthetic Biology},
	publisher = {American Chemical Society},
	doi = {https://doi.org/10.1021/acssynbio.3c00662},
	url = {https://doi.org/10.1021/acssynbio.3c00662},
	urldate = {2024-04-10},
	abstract = {This paper presents Maud, a command-line application that
	            implements Bayesian statistical inference for kinetic models of
	            biochemical metabolic reaction networks. Maud takes into account
	            quantitative information from omics experiments and background
	            knowledge as well as structural information about kinetic
	            mechanisms, regulatory interactions, and enzyme knockouts. Our
	            paper reviews the existing options in this area, presents a case
	            study illustrating how Maud can be used to analyze a metabolic
	            network, and explains the biological, statistical, and
	            computational design decisions underpinning Maud.},
}

@misc{leeftinkProbabilisticPontryaginsMaximum2025a,
  title = {Probabilistic Pontryagin's Maximum Principle for Continuous-Time Model-Based Reinforcement Learning},
  author = {Leeftink, David and Y{\i}ld{\i}z, {\c C}a{\u g}atay and Ridderbusch, Steffen and Hinne, Max and van Gerven, Marcel},
  year = {2025},
  month = apr,
  number = {arXiv:2504.02543},
  eprint = {2504.02543},
  primaryclass = {cs},
  publisher = {arXiv},
  doi = {https://doi.org/10.48550/arXiv.2504.02543},
  url = {http://arxiv.org/abs/2504.02543},
  urldate = {2025-05-09},
  abstract = {Without exact knowledge of the true system dynamics, optimal control of non-linear continuous-time systems requires careful treatment of epistemic uncertainty. In this work, we propose a probabilistic extension to Pontryagin's maximum principle by minimizing the mean Hamiltonian with respect to epistemic uncertainty. We show minimization of the mean Hamiltonian is a necessary optimality condition when optimizing the mean cost, and propose a multiple shooting numerical method scalable to large-scale probabilistic dynamical models, including ensemble neural ordinary differential equations. Comparisons against state-of-the-art methods in online and offline model-based reinforcement learning tasks show that our probabilistic Hamiltonian formulation leads to reduced trial costs in offline settings and achieves competitive performance in online scenarios. By bridging optimal control and reinforcement learning, our approach offers a principled and practical framework for controlling uncertain systems with learned dynamics.},
  archiveprefix = {arXiv},
  keywords = {Computer Science - Machine Learning},
}

@article{hoffmanNoUTurnSamplerAdaptively2014,
	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 = {1593--1623},
	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},
}

@misc{timonenImportanceSamplingApproach2022,
	title = {An Importance Sampling Approach for Reliable and Efficient
	         Inference in Bayesian Ordinary Differential Equation Models},
	author = {Timonen, Juho and Siccha, Nikolas and Bales, Ben and Lähdesmäki, Harri and Vehtari, Aki},
	year = {2022},
	month = may,
	number = {arXiv:2205.09059},
	eprint = {2205.09059},
	primaryclass = {stat},
	publisher = {arXiv},
	doi = {https://doi.org/10.48550/arXiv.2205.09059},
	url = {http://arxiv.org/abs/2205.09059},
	urldate = {2023-10-20},
	abstract = {Statistical models can involve implicitly defined quantities,
	            such as solutions to nonlinear ordinary differential equations
	            (ODEs), that unavoidably need to be numerically approximated in
	            order to evaluate the model. The approximation error inherently
	            biases statistical inference results, but the amount of this bias
	            is generally unknown and often ignored in Bayesian parameter
	            inference. We propose a computationally efficient method for
	            verifying the reliability of posterior inference for such models,
	            when the inference is performed using Markov chain Monte Carlo
	            methods. We validate the efficiency and reliability of our
	            workflow in experiments using simulated and real data, and
	            different ODE solvers. We highlight problems that arise with
	            commonly used adaptive ODE solvers, and propose robust and
	            effective alternatives which, accompanied by our workflow, can
	            now be taken into use without losing reliability of the
	            inferences.},
	archiveprefix = {arXiv},
	keywords = {Statistics - Computation},
}

@article{margossianReviewAutomaticDifferentiation2019,
	title = {A Review of Automatic Differentiation and Its Efficient
	         Implementation},
	author = {Margossian, Charles C.},
	year = {2019},
	month = jul,
	journal = {WIREs Data Mining and Knowledge Discovery},
	volume = {9},
	number = {4},
	eprint = {1811.05031},
	issn = {1942-4787, 1942-4795},
	doi = {https://doi.org/10.1002/WIDM.1305},
	url = {http://arxiv.org/abs/1811.05031},
	urldate = {2020-02-08},
	abstract = {Derivatives play a critical role in computational statistics,
	            examples being Bayesian inference using Hamiltonian Monte Carlo
	            sampling and the training of neural networks. Automatic
	            differentiation is a powerful tool to automate the calculation of
	            derivatives and is preferable to more traditional methods,
	            especially when differentiating complex algorithms and
	            mathematical functions. The implementation of automatic
	            differentiation however requires some care to insure efficiency.
	            Modern differentiation packages deploy a broad range of
	            computational techniques to improve applicability, run time, and
	            memory management. Among these techniques are operation
	            overloading, regionbased memory, and expression templates. There
	            also exist several mathematical techniques which can yield high
	            performance gains when applied to complex algorithms. For example
	            , semi-analytical derivatives can reduce by orders of magnitude
	            the runtime required to numerically solve and differentiate an
	            algebraic equation. Open and practical problems include the
	            extension of current packages to provide more specialized
	            routines, and finding optimal methods to perform higher-order
	            differentiation.},
	archiveprefix = {arXiv},
	langid = {english},
	keywords = {Computer Science - Mathematical Software,Statistics -
	            Computation},
}


@misc{mangoubiDoesHamiltonianMonte2018,
  title = {Does Hamiltonian Monte Carlo Mix Faster than a Random Walk on Multimodal Densities?},
  author = {Mangoubi, Oren and Pillai, Natesh S. and Smith, Aaron},
  year = {2018},
  month = sep,
  number = {arXiv:1808.03230},
  eprint = {1808.03230},
  primaryclass = {cs, math, stat},
  publisher = {arXiv},
  url = {http://arxiv.org/abs/1808.03230},
  doi = {https://doi.org/10.48550/arXiv.1808.03230},
  urldate = {2024-01-11},
  abstract = {Hamiltonian Monte Carlo (HMC) is a very popular and generic collection of Markov chain Monte Carlo (MCMC) algorithms. One explanation for the popularity of HMC algorithms is their excellent performance as the dimension d of the target becomes large: under conditions that are satisfied for many common statistical models, optimally-tuned HMC algorithms have a running time that scales like d0.25. In stark contrast, the running time of the usual Random-Walk Metropolis (RWM) algorithm, optimally tuned, scales like d. This superior scaling of the HMC algorithm with dimension is attributed to the fact that it, unlike RWM, incorporates the gradient information in the proposal distribution. In this paper, we investigate a different scaling question: does HMC beat RWM for highly multimodal targets? We find that the answer is often no. We compute the spectral gaps for both the algorithms for a specific class of multimodal target densities, and show that they are identical. The key reason is that, within one mode, the gradient is effectively ignorant about other modes, thus negating the advantage the HMC algorithm enjoys in unimodal targets. We also give heuristic arguments suggesting that the above observation may hold quite generally. Our main tool for answering this question is a novel simple formula for the conductance of HMC using Liouville's theorem. This result allows us to compute the spectral gap of HMC algorithms, for both the classical HMC with isotropic momentum and the recent Riemannian HMC, for multimodal targets.},
  archiveprefix = {arXiv},
  langid = {english},
  keywords = {Computer Science - Machine Learning,Mathematics - Probability,Statistics - Computation,Statistics - Machine Learning,Statistics - Methodology},
}

@article{carpenterStanProbabilisticProgramming2017,
  title = {Stan: A Probabilistic Programming Language},
  shorttitle = {Stan},
  author = {Carpenter, Bob and Gelman, Andrew and Hoffman, Matthew D. and Lee, Daniel and Goodrich, Ben and Betancourt, Michael and Brubaker, Marcus and Guo, Jiqiang and Li, Peter and Riddell, Allen},
  year = {2017},
  month = jan,
  journal = {Journal of Statistical Software},
  volume = {76},
  number = {1},
  pages = {1--32},
  issn = {1548-7660},
  doi = {https://doi.org/10.18637/jss.v076.i01},
  url = {https://www.jstatsoft.org/index.php/jss/article/view/v076i01},
  urldate = {2020-08-27},
  copyright = {Copyright (c) 2017 Bob Carpenter, Andrew Gelman, Matthew D. Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, Allen Riddell},
  langid = {english},
  keywords = {algorithmic differentiation,Bayesian inference,probabilistic programming,Stan},
}

@article{abril-plaPyMCModernComprehensive2023,
  title = {PyMC: A Modern, and Comprehensive Probabilistic Programming Framework in Python},
  shorttitle = {PyMC},
  author = {Abril-Pla, Oriol and Andreani, Virgile and Carroll, Colin and Dong, Larry and Fonnesbeck, Christopher J. and Kochurov, Maxim and Kumar, Ravin and Lao, Junpeng and Luhmann, Christian C. and Martin, Osvaldo A. and Osthege, Michael and Vieira, Ricardo and Wiecki, Thomas and Zinkov, Robert},
  year = {2023},
  month = sep,
  journal = {PeerJ Computer Science},
  volume = {9},
  pages = {e1516},
  issn = {2376-5992},
  doi = {https://doi.org/10.7717/peerj-cs.1516},
  url = {https://peerj.com/articles/cs-1516},
  urldate = {2024-11-15},
  abstract = {PyMC is a probabilistic programming library for Python that provides tools for constructing and fitting Bayesian models. It offers an intuitive, readable syntax that is close to the natural syntax statisticians use to describe models. PyMC leverages the symbolic computation library PyTensor, allowing it to be compiled into a variety of computational backends, such as C, JAX, and Numba, which in turn offer access to different computational architectures including CPU, GPU, and TPU. Being a general modeling framework, PyMC supports a variety of models including generalized hierarchical linear regression and classification, time series, ordinary differential equations (ODEs), and non-parametric models such as Gaussian processes (GPs). We demonstrate PyMC's versatility and ease of use with examples spanning a range of common statistical models. Additionally, we discuss the positive role of PyMC in the development of the open-source ecosystem for probabilistic programming.},
  copyright = {https://creativecommons.org/licenses/by/4.0/},
  langid = {english}
}

@article{casellaChoiceInitialGuesses2021,
	title = {On the Choice of Initial Guesses for the Newton-Raphson
	         Algorithm},
	author = {Casella, Francesco and Bachmann, Bernhard},
	year = {2021},
	month = jun,
	journal = {Applied Mathematics and Computation},
	volume = {398},
	pages = {125991},
	issn = {0096-3003},
	doi = {https://doi.org/10.1016/j.amc.2021.125991},
	url = {https://www.sciencedirect.com/science/article/pii/S0096300321000394},
	urldate = {2024-11-01},
	abstract = {The initialization of equation-based differential-algebraic
	            system models, and more in general the solution of many
	            engineering and scientific problems, require the solution of
	            systems of nonlinear equations. Newton-Raphson's method is widely
	            used for this purpose; it is very efficient in the computation of
	            the solution if the initial guess is close enough to it, but it
	            can fail otherwise. In this paper, several criteria are
	            introduced to analyze the influence of the initial guess on the
	            evolution of Newton-Raphson's algorithm and to identify which
	            initial guesses need to be improved in case of convergence
	            failure. In particular, indicators based on first and second
	            derivatives of the residual function are introduced, whose values
	            allow to assess how much the initial guess of each variable can
	            be responsible for the convergence failure. The use of such
	            criteria, which are based on rigorously proven results, is
	            successfully demonstrated in three exemplary test cases.},
	keywords = {Convergence,Equation-based modelling,Newton-Raphson's algorithm,
	            Nonlinear equations},
}

@misc{StanReferenceManual,
	title = {Stan Reference Manual, 2.37},
	author = {Stan Development Team},
	year = {2026},
	url = {https://mc-stan.org},
}

@misc{StanUsersGuide,
	title = {Stan User's Guide, 2.37},
	author = {Stan Development Team},
	year = {2026},
	url = {https://mc-stan.org},
}

@article{swopeComputerSimulationMethod1982,
  title = {A Computer Simulation Method for the Calculation of Equilibrium Constants for the Formation of Physical Clusters of Molecules: Application to Small Water Clusters},
  shorttitle = {A Computer Simulation Method for the Calculation of Equilibrium Constants for the Formation of Physical Clusters of Molecules},
  author = {Swope, William C. and Andersen, Hans C. and Berens, Peter H. and Wilson, Kent R.},
  year = {1982},
  month = jan,
  journal = {The Journal of Chemical Physics},
  volume = {76},
  number = {1},
  pages = {637--649},
  issn = {0021-9606},
  doi = {https://doi.org/10.1063/1.442716},
  url = {https://doi.org/10.1063/1.442716},
  urldate = {2025-05-09},
  abstract = {We present a molecular dynamics computer simulation method for calculating equilibrium constants for the formation of physical clusters of molecules. The method is based on Hill's formal theory of physical clusters. In the method, a molecular dynamics calculation is used to calculate the average potential energy of a cluster of molecules as a function of temperature, and the equilibrium constants are calculated from the integral of the energy with respect to reciprocal temperature. The method is illustrated by calculations of the equilibrium constants for the formation of clusters of two to five water molecules that interact with each other by an intermolecular potential devised by Watts. The method is compared with other procedures for calculating the thermodynamic properties of clusters.},
}

@misc{blanesNumericalIntegratorsHybrid2014,
	title = {Numerical Integrators for the Hybrid Monte Carlo Method},
	author = {Blanes, Sergio and Casas, Fernando and Sanz-Serna, J. M.},
	year = {2014},
	month = may,
	number = {arXiv:1405.3153},
	eprint = {1405.3153},
	publisher = {arXiv},
	doi = {https://doi.org/10.48550/arXiv.1405.3153},
	url = {http://arxiv.org/abs/1405.3153},
	urldate = {2024-10-24},
	abstract = {We construct numerical integrators for Hamiltonian problems that
	            may advantageously replace the standard Verlet time-stepper
	            within Hybrid Monte Carlo and related simulations. Past attempts
	            have often aimed at boosting the order of accuracy of the
	            integrator and/or reducing the size of its error constants; order
	            and error constant are relevant concepts in the limit of
	            vanishing step-length. We propose an alternative methodology
	            based on the performance of the integrator when sampling from
	            Gaussian distributions with not necessarily small step-lengths.
	            We construct new splitting formulae that require two, three or
	            four force evaluations per time-step. Limited, proof-of-concept
	            numerical experiments suggest that the new integrators may
	            provide an improvement on the efficiency of the standard Verlet
	            method, especially in problems with high dimensionality.},
	archiveprefix = {arXiv},
	keywords = {Mathematics - Numerical Analysis},
}

@article{kokLocatingCharacterizingStationary2009,
	title = {Locating and Characterizing the Stationary Points of the 
	         Extended Rosenbrock Function},
	author = {Kok, Schalk and Sandrock, Carl},
	year = {2009},
	month = sep,
	journal = {Evolutionary Computation},
	volume = {17},
	number = {3},
	pages = {437--453},
	issn = {1063-6560},
	doi = {https://doi.org/10.1162/evco.2009.17.3.437},
	url = {https://doi.org/10.1162/evco.2009.17.3.437},
	urldate = {2025-01-10},
	abstract = {Two variants of the extended Rosenbrock function are analyzed in
	            order to find the stationary points. The first variant is shown
	            to possess a single stationary point, the global minimum. The
	            second variant has numerous stationary points for high
	            dimensionality. A previously proposed method is shown to be
	            numerically intractable, requiring arbitrary precision
	            computation in many cases to enumerate candidate solutions.
	            Instead, a standard Newtonian method with multi-start is applied
	            to locate stationary points. The relative magnitude of the
	            negative and positive eigenvalues of the Hessian is also computed
	            , in order to characterize the saddle points. For dimensions up
	            to 100, only two local minimizers are found, but many saddle
	            points exist. Two saddle points with a single negative eigenvalue
	            exist for high dimensionality, which may appear as ``near'' local
	            minima. The remaining saddle points we found have a predictable
	            form, and a method is proposed to estimate their number. Monte
	            Carlo simulation indicates that it is unlikely to escape these
	            saddle points using uniform random search. A standard particle
	            swarm algorithm also struggles to improve upon a saddle point
	            contained within the initial population.},
}
@article{rosenbrockAutomaticMethodFinding1960,
	title = {An Automatic Method for Finding the Greatest or Least
	         Value of a Function},
	author = {Rosenbrock, H. H.},
	year = {1960},
	month = {jan},
	journal = {The Computer Journal},
	volume = {3},
	number = {3},
	pages = {175-184},
	issn = {0010-4620},
	doi = {https://doi.org/10.1093/comjnl/3.3.175},
	url = {https://doi.org/10.1093/comjnl/3.3.175},
	urldate = {2025-01-10},
	abstract = {The greatest or least value of a function of several variables
	            is to be found when the variables are restricted to a given
	            region. A method is developed for dealing with this problem and
	            is compared with possible alternatives. The method can be used on
	            a digital computer, and is incorporated in a program for Mercury.
	            },
}

@article{kumarArviZUnifiedLibrary2019,
	title = {ArviZ a Unified Library for Exploratory Analysis of Bayesian
	          Models in Python},
	author = {Kumar, Ravin and Carroll, Colin and Hartikainen, Ari and Martin,
	          Osvaldo},
	year = {2019},
	month = jan,
	journal = {Journal of Open Source Software},
	volume = {4},
	number = {33},
	pages = {1143},
	issn = {2475-9066},
	doi = {https://doi.org/10.21105/joss.01143},
	url = {http://joss.theoj.org/papers/10.21105/joss.01143},
	urldate = {2021-12-02},
	abstract = {While conceptually simple, Bayesian methods can be
	            mathematically and numerically challenging. Probabilistic
	            programming languages (PPLs) implement functions to easily build
	            Bayesian models together with efficient automatic inference
	            methods. This helps separate the model building from the
	            inference, allowing practitioners to focus on their specific
	            problems and leaving PPLs to handle the computational details for
	            them (Bessiere, Mazer, Ahuactzin, \& Mekhnacha, 2013; Daniel Roy,
	            2015; Ghahramani, 2015). The inference process generates a
	            posterior distribution --- which has a central role in Bayesian
	            statistics --- together with other distributions like the
	            posterior predictive distribution and the prior predictive
	            distribution. The correct visualization, analysis, and
	            interpretation of these distributions is key to properly answer
	            the questions that motivate the inference process.},
	langid = {english},
}


@article{oliveiraImplicitInverseFunction2014,
  title = {The Implicit and the Inverse Function Theorems: Easy Proofs},
  shorttitle = {The Implicit and the Inverse Function Theorems},
  author = {de Oliveira, Oswaldo Rio Branco},
  year = {2014},
  journal = {Real Analysis Exchange},
  volume = {39},
  number = {1},
  eprint = {1212.2066},
  primaryclass = {math},
  pages = {207},
  issn = {01471937},
  doi = {https://doi.org/10.14321/realanalexch.39.1.0207},
  url = {http://arxiv.org/abs/1212.2066},
  urldate = {2025-06-13},
  abstract = {This article presents simple and easy proofs of the Implicit Function Theorem and the Inverse Function Theorem, in this order, both of them on a finite-dimensional Euclidean space, that employ only the Intermediate Value Theorem and the Mean-Value Theorem. These proofs avoid compactness arguments, the contraction principle, and fixed-point theorems.},
  archiveprefix = {arXiv},
  langid = {english},
  keywords = {Mathematics - Classical Analysis and ODEs},
}

@misc{benTalNemirovskiLectureNotes,
  title = {Lecture Notes: Optimization III},
  author = {Ben-Tal, Aharon and Nemirovski, Arkadi},
  year = {2023},
  url = {https://www2.isye.gatech.edu/~nemirovs/OPTIIILN2023Spring.pdf},
}

@misc{cabezas2024blackjax,
	title = {BlackJAX: Composable Bayesian Inference in JAX},
	author = {Cabezas, Alberto and Corenflos, Adrien and Lao, Junpeng and Louf,
	          Rémi},
	year = {2024},
	eprint = {2402.10797},
	doi = {https://doi.org/10.48550/arXiv.2402.10797},
	primaryclass = {cs.MS},
	archiveprefix = {arXiv},
}

@misc{jax2018github,
	title = {JAX: Composable Transformations of Python+NumPy Programs},
	author = {Bradbury, James and Frostig, Roy and Hawkins, Peter and Johnson,
	          Matthew James and Leary, Chris and Maclaurin, Dougal and Necula,
	          George and Paszke, Adam and VanderPlas, Jake and Wanderman-Milne,
	          Skye and Zhang, Qiao},
	year = {2018},
	url = {http://github.com/jax-ml/jax},
}

@misc{bayeuxdevelopersBayeuxStateArt2025,
	title = {Bayeux: State of the Art Inference for Your Bayesian Models},
	shorttitle = {Bayeux},
	author = {Bayeux developers},
	year = {2025},
	url = {https://github.com/jax-ml/bayeux},
}

@article{optimistix2024,
	title = {Optimistix: Modular Optimisation in JAX and Equinox},
	author = {Rader, Jason and Lyons, Terry and Kidger, Patrick},
	year = {2024},
	journal = {arXiv:2402.09983},
	eprint = {2402.09983},
	archiveprefix = {arXiv},
	doi = {https://doi.org/10.48550/arXiv.2402.09983},
	url = {https://doi.org/10.48550/arXiv.2402.09983}
}

@phdthesis{kidger2021on,
	title = {On Neural Differential Equations},
	author = {Kidger, Patrick},
	year = {2021},
	school = {University of Oxford},
	url = {https://arxiv.org/abs/2202.02435},
	doi = {https://doi.org/10.48550/arXiv.2202.02435}
}

@misc{simulationlib,
  title = {Virtual Library of Simulation Experiments: Test Functions and Datasets},
  author = {Surjanovic, S. and Bingham, D.},
  url = {http://www.sfu.ca/{\textasciitilde}ssurjano}
}

@article{matosGRASPComputationalPlatform2022,
	title = {GRASP: A Computational Platform for Building Kinetic Models of
	         Cellular Metabolism},
	shorttitle = {GRASP},
	author = {Matos, Marta R A and Saa, Pedro A and Cowie, Nicholas and Volkova,
	          Svetlana and de Leeuw, Marina and Nielsen, Lars K},
	year = {2022},
	month = jan,
	journal = {Bioinformatics Advances},
	volume = {2},
	number = {1},
	pages = {vbac066},
	issn = {2635-0041},
	doi = {https://doi.org/10.1093/bioadv/vbac066},
	url = {https://doi.org/10.1093/bioadv/vbac066},
	urldate = {2023-10-26},
	abstract = {Kinetic models of metabolism are crucial to understand the inner
	            workings of cell metabolism. By taking into account enzyme
	            regulation, detailed kinetic models can provide accurate
	            predictions of metabolic fluxes. Comprehensive consideration of
	            kinetic regulation requires highly parameterized non-linear
	            models, which are challenging to build and fit using available
	            modelling tools. Here, we present a computational package
	            implementing the GRASP framework for building detailed kinetic
	            models of cellular metabolism. By defining the mechanisms of
	            enzyme regulation and a reference state described by reaction
	            fluxes and their corresponding Gibbs free energy ranges, GRASP
	            can efficiently sample an arbitrarily large population of
	            thermodynamically feasible kinetic models. If additional
	            experimental data are available (fluxes, enzyme and metabolite
	            concentrations), these can be integrated to generate models that
	            closely reproduce these observations using an approximate
	            Bayesian computation fitting framework. Within the same framework
	            , model selection tasks can be readily performed.GRASP is
	            implemented as an open-source package in the MATLAB environment.
	            The software runs in Windows, macOS and Linux, is documented
	            (graspk.readthedocs.io) and unit-tested. GRASP is freely
	            available at github.com/biosustain/GRASP.Supplementary data are
	            available at Bioinformatics Advances online.},
}

@article{fiedlerTailoredParameterOptimization2016,
	title = {Tailored Parameter Optimization Methods for Ordinary Differential
	         Equation Models with Steady-State Constraints},
	author = {Fiedler, Anna and Raeth, Sebastian and Theis, Fabian J. and
	          Hausser, Angelika and Hasenauer, Jan},
	year = {2016},
	month = aug,
	journal = {BMC Systems Biology},
	volume = {10},
	number = {1},
	pages = {80},
	issn = {1752-0509},
	doi = {https://doi.org/10.1186/s12918-016-0319-7},
	url = {https://doi.org/10.1186/s12918-016-0319-7},
	urldate = {2025-01-29},
	abstract = {Ordinary differential equation (ODE) models are widely used to
	            describe (bio-)chemical and biological processes. To enhance the
	            predictive power of these models, their unknown parameters are
	            estimated from experimental data. These experimental data are
	            mostly collected in perturbation experiments, in which the
	            processes are pushed out of steady state by applying a stimulus.
	            The information that the initial condition is a steady state of
	            the unperturbed process provides valuable information, as it
	            restricts the dynamics of the process and thereby the parameters.
	            However, implementing steady-state constraints in the
	            optimization often results in convergence problems.},
	keywords = {Differential equation,Parameter optimization,Perturbation
	            experiments,Steady state},
}

@article{lakrisenkoEfficientComputationAdjoint2023,
	title = {Efficient Computation of Adjoint Sensitivities at Steady-State in 
	         ODE Models of Biochemical Reaction Networks},
	author = {Lakrisenko, Polina and Stapor, Paul and Grein, Stephan and
	          Paszkowski, {\L}ukasz and Pathirana, Dilan and Fr{\"o}hlich, Fabian
	          and Lines, Glenn Terje and Weindl, Daniel and Hasenauer, Jan},
	year = {2023},
	month = jan,
	journal = {PLOS Computational Biology},
	volume = {19},
	number = {1},
	pages = {e1010783},
	publisher = {Public Library of Science},
	issn = {1553-7358},
	doi = {https://doi.org/10.1371/journal.pcbi.1010783},
	url = {
	       https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1010783
	       },
	urldate = {2025-01-09},
	abstract = {Dynamical models in the form of systems of ordinary differential
	            equations have become a standard tool in systems biology. Many
	            parameters of such models are usually unknown and have to be
	            inferred from experimental data. Gradient-based optimization has
	            proven to be effective for parameter estimation. However,
	            computing gradients becomes increasingly costly for larger models
	            , which are required for capturing the complex interactions of
	            multiple biochemical pathways. Adjoint sensitivity analysis has
	            been pivotal for working with such large models, but methods
	            tailored for steady-state data are currently not available. We
	            propose a new adjoint method for computing gradients, which is
	            applicable if the experimental data include steady-state
	            measurements. The method is based on a reformulation of the
	            backward integration problem to a system of linear algebraic
	            equations. The evaluation of the proposed method using real-world
	            problems shows a speedup of total simulation time by a factor of
	            up to 4.4. Our results demonstrate that the proposed approach can
	            achieve a substantial improvement in computation time, in
	            particular for large-scale models, where computational efficiency
	            is critical.},
	langid = {english},
	keywords = {Biochemical simulations,Differential equations,Dynamical systems
	            ,Integrals,Numerical integration,Optimization,Simulation and
	            modeling,Time measurement},
}

@incollection{nealMCMCUsingHamiltonian2011,
  title = {MCMC Using Hamiltonian Dynamics},
  booktitle = {Handbook of Markov Chain Monte Carlo},
  author = {Neal, Radford},
  editor = {Brooks, Steve and Gelman, Andrew and Jones, Galin and Meng, Xiao-Li},
  year = {2011},
  month = {may},
  volume = {20116022},
  publisher = {Chapman and Hall/CRC},
  doi = {https://doi.org/10.1201/b10905-6},
  url = {http://www.crcnetbase.com/doi/abs/10.1201/b10905-6},
  urldate = {2022-09-29},
  isbn = {978-1-4200-7941-8 978-1-4200-7942-5},
  langid = {english},
}

@article{betancourtConceptualIntroductionHamiltonian2018,
  title = {A Conceptual Introduction to Hamiltonian Monte Carlo},
  author = {Betancourt, Michael},
  year = {2018},
  month = {Jul},
  journal = {arXiv:1701.02434 [stat]},
  eprint = {1701.02434},
  primaryclass = {stat},
  url = {http://arxiv.org/abs/1701.02434},
  doi = {https://doi.org/10.48550/arXiv.1701.02434},
  urldate = {2020-09-28},
  abstract = {Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice. Unfortunately, that understanding is confined within the mathematics of differential geometry which has limited its dissemination, especially to the applied communities for which it is particularly important.},
  archiveprefix = {arXiv},
  langid = {english},
  keywords = {Statistics - Methodology},
}
@book{allgowerIntroductionNumericalContinuation2003,
  title = {Introduction to Numerical Continuation Methods},
  author = {Allgower, Eugene L. and Georg, Kurt},
  year = 2003,
  month = jan,
  publisher = {Society for Industrial and Applied Mathematics},
  doi = {https://doi.org/10.1137/1.9780898719154},
  url = {http://epubs.siam.org/doi/book/10.1137/1.9780898719154},
  urldate = {2026-01-13},
  isbn = {978-0-89871-544-6 978-0-89871-915-4},
  langid = {english},
}

@incollection{diehlEfficientNumericalMethods2009,
  title = {Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation},
  booktitle = {Nonlinear Model Predictive Control: Towards New Challenging Applications},
  author = {Diehl, Moritz and Ferreau, Hans Joachim and Haverbeke, Niels},
  editor = {Magni, Lalo and Raimondo, Davide Martino and Allgöwer, Frank},
  year = 2009,
  pages = {391--417},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  doi = {https://doi.org/10.1007/978-3-642-01094-1_32},
  url = {https://doi.org/10.1007/978-3-642-01094-1\_32},
  urldate = {2026-01-13},
  abstract = {This overview paper reviews numerical methods for solution of optimal control problems in real-time, as they arise in nonlinear model predictive control (NMPC) as well as in moving horizon estimation (MHE). In the first part, we review numerical optimal control solution methods, focussing exclusively on a discrete time setting. We discuss several algorithmic ''building blocks'' that can be combined to a multitude of algorithms. We start by discussing the sequential and simultaneous approaches, the first leading to smaller, the second to more structured optimization problems. The two big families of Newton type optimization methods, Sequential Quadratic Programming (SQP) and Interior Point (IP) methods, are presented, and we discuss how to exploit the optimal control structure in the solution of the linear-quadratic subproblems, where the two major alternatives are ``condensing'' and band structure exploiting approaches. The second part of the paper discusses how the algorithms can be adapted to the real-time challenge of NMPC and MHE. We recall an important sensitivity result from parametric optimization, and show that a tangential solution predictor for online data can easily be generated in Newton type algorithms. We point out one important difference between SQP and IP methods: while both methods are able to generate the tangential predictor for fixed active sets, the SQP predictor even works across active set changes. We then classify many proposed real-time optimization approaches from the literature into the developed categories.},
  isbn = {978-3-642-01094-1},
  langid = {english},
  keywords = {Newton type methods,numerical optimal control,real-time optimization,structure exploitation},
}

@inproceedings{pmlr-v108-lorraine20a,
  title = {Optimizing Millions of Hyperparameters by Implicit Differentiation},
  booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics},
  author = {Lorraine, Jonathan and Vicol, Paul and Duvenaud, David},
  editor = {Chiappa, Silvia and Calandra, Roberto},
  year = 2020,
  month = aug,
  series = {Proceedings of Machine Learning Research},
  volume = {108},
  pages = {1540--1552},
  publisher = {PMLR},
  url = {https://proceedings.mlr.press/v108/lorraine20a.html},
  abstract = {We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network---where every weight is a hyperparameter tuned for validation performance---outputting augmented training examples. Jointly tuning weights and hyper-parameters is only a few times more costly in memory and compute than standard training.},
  file = {/Users/tedgro/Zotero/storage/CKWFZCPG/lorraine20a.pdf}
}

