@article{todorov2009efficient,
  title={Efficient computation of optimal actions},
  author={Todorov, Emanuel},
  journal={Proceedings of the national academy of sciences},
  volume={106},
  number={28},
  pages={11478--11483},
  year={2009},
  publisher={National Acad Sciences}
}

@book{graham2013stochastic,
  title={Stochastic simulation and Monte Carlo methods: mathematical foundations of stochastic simulation},
  author={Graham, Carl and Talay, Denis},
  volume={68},
  year={2013},
  publisher={Springer Science \& Business Media}
}

@article{jin2022minimax,
  title={Minimax Optimal Kernel Operator Learning via Multilevel Training},
  author={Jin, Jikai and Lu, Yiping and Blanchet, Jose and Ying, Lexing},
  journal={arXiv preprint arXiv:2209.14430},
  year={2022}
}

@article{demange2022efficient,
  title={Efficient estimation of multiple expectations with the same sample by adaptive importance sampling and control variates},
  author={Demange-Chryst, Julien and Bachoc, Fran{\c{c}}ois and Morio, J{\'e}r{\^o}me},
  journal={arXiv preprint arXiv:2212.00568},
  year={2022}
}
@article{giles2015multilevel,
  title={Multilevel monte carlo methods},
  author={Giles, Michael B},
  journal={Acta numerica},
  volume={24},
  pages={259--328},
  year={2015},
  publisher={Cambridge University Press}
}


@article{becker2022learning,
  title={Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing},
  author={Becker, Sebastian and Jentzen, Arnulf and M{\"u}ller, Marvin S and von Wurstemberger, Philippe},
  journal={arXiv preprint arXiv:2202.02717},
  year={2022}
}


@article{zhang2014applications,
  title={Applications of the cross-entropy method to importance sampling and optimal control of diffusions},
  author={Zhang, Wei and Wang, Han and Hartmann, Carsten and Weber, Marcus and Schütte, Christof},
  journal={SIAM Journal on Scientific Computing},
  volume={36},
  number={6},
  pages={A2654--A2672},
  year={2014},
  publisher={SIAM}
}


@inproceedings{alvarez2021dataset,
  title={Dataset dynamics via gradient flows in probability space},
  author={Alvarez-Melis, David and Fusi, Nicol{\`o}},
  booktitle={International Conference on Machine Learning},
  pages={219--230},
  year={2021},
  organization={PMLR}
}

@article{benamou2015iterative,
  title={Iterative Bregman projections for regularized transportation problems},
  author={Benamou, Jean-David and Carlier, Guillaume and Cuturi, Marco and Nenna, Luca and Peyr{\'e}, Gabriel},
  journal={SIAM Journal on Scientific Computing},
  volume={37},
  number={2},
  pages={A1111--A1138},
  year={2015},
  publisher={SIAM}
}


@article{bakhos2015fast,
  title={A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers},
  author={Bakhos, Tania and Saibaba, Arvind K and Kitanidis, Peter K},
  journal={Journal of computational Physics},
  volume={299},
  pages={940--954},
  year={2015},
  publisher={Elsevier}
}


@article{bruna2022neural,
  title={Neural Galerkin Scheme with Active Learning for High-Dimensional Evolution Equations},
  author={Bruna, Joan and Peherstorfer, Benjamin and Vanden-Eijnden, Eric},
  journal={arXiv preprint arXiv:2203.01360},
  year={2022}
}

@book{sarkka2019applied,
  title={Applied stochastic differential equations},
  author={S{\"a}rkk{\"a}, Simo and Solin, Arno},
  volume={10},
  year={2019},
  publisher={Cambridge University Press}
}

@article{raissi2019686,
title = {Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
journal = {Journal of Computational Physics},
volume = {378},
pages = {686-707},
year = {2019},
issn = {0021-9991},
doi = {https://doi.org/10.1016/j.jcp.2018.10.045},
url = {https://www.sciencedirect.com/science/article/pii/S0021999118307125},
author = {M. Raissi and P. Perdikaris and G.E. Karniadakis},
keywords = {Data-driven scientific computing, Machine learning, Predictive modeling, Runge–Kutta methods, Nonlinear dynamics},
}

@article{SAMANIEGO2020112790,
title = {An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {362},
pages = {112790},
year = {2020},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2019.112790},
url = {https://www.sciencedirect.com/science/article/pii/S0045782519306826},
author = {E. Samaniego and C. Anitescu and S. Goswami and V.M. Nguyen-Thanh and H. Guo and K. Hamdia and X. Zhuang and T. Rabczuk},
keywords = {Physics informed, Deep neural networks, Energy approach},
}

@article{doi:10.1137/19M1274067,
author = {Lu, Lu and Meng, Xuhui and Mao, Zhiping and Karniadakis, George Em},
title = {DeepXDE: A Deep Learning Library for Solving Differential Equations},
journal = {SIAM Review},
volume = {63},
number = {1},
pages = {208-228},
year = {2021},
doi = {10.1137/19M1274067},
URL = {https://doi.org/10.1137/19M1274067},
eprint = {https://doi.org/10.1137/19M1274067}
}

@article{PSAROS2022111121,
title = {Meta-learning PINN loss functions},
journal = {Journal of Computational Physics},
volume = {458},
pages = {111121},
year = {2022},
issn = {0021-9991},
doi = {https://doi.org/10.1016/j.jcp.2022.111121},
url = {https://www.sciencedirect.com/science/article/pii/S0021999122001838},
author = {Apostolos F Psaros and Kenji Kawaguchi and George Em Karniadakis},
keywords = {Physics-informed neural networks, Meta-learning, Meta-learned loss function}
}

@article{Beck2021OnNF,
  title={On nonlinear Feynman–Kac formulas for viscosity solutions of semilinear parabolic partial differential equations},
  author={Christian Beck and Martin Hutzenthaler and Arnulf Jentzen},
  journal={Stochastics and Dynamics},
  year={2021}
}

@article{Han2018SolvingHP,
  title={Solving high-dimensional partial differential equations using deep learning},
  author={Jiequn Han and Arnulf Jentzen and Weinan E},
  journal={Proceedings of the National Academy of Sciences},
  year={2018},
  volume={115},
  pages={8505 - 8510}
}

@article{Song2021ScoreBasedGM,
  title={Score-Based Generative Modeling through Stochastic Differential Equations},
  author={Yang Song and Jascha Narain Sohl-Dickstein and Diederik P. Kingma and Abhishek Kumar and Stefano Ermon and Ben Poole},
  journal={ArXiv},
  year={2021},
  volume={abs/2011.13456}
}

@inproceedings{Huang2021AVP,
  title={A Variational Perspective on Diffusion-Based Generative Models and Score Matching},
  author={Chin-Wei Huang and Jae Hyun Lim and Aaron C. Courville},
  booktitle={NeurIPS},
  year={2021}
}

@inproceedings{Vahdat2021ScorebasedGM,
  title={Score-based Generative Modeling in Latent Space},
  author={Arash Vahdat and Karsten Kreis and Jan Kautz},
  booktitle={NeurIPS},
  year={2021}
}

@article{Lake2011OneSL,
  title={One shot learning of simple visual concepts},
  author={Brenden M. Lake and Ruslan Salakhutdinov and Jason Gross and Joshua B. Tenenbaum},
  journal={Cognitive Science},
  year={2011},
  volume={33}
}

@article{JimenezRezende2016OneShotGI,
  title={One-Shot Generalization in Deep Generative Models},
  author={Danilo Jimenez Rezende and Shakir Mohamed and Ivo Danihelka and Karol Gregor and Daan Wierstra},
  journal={ArXiv},
  year={2016},
  volume={abs/1603.05106}
}

@article{Cloutre2019FIGRFI,
  title={FIGR: Few-shot Image Generation with Reptile},
  author={Louis Clou{\^a}tre and Marc Demers},
  journal={ArXiv},
  year={2019},
  volume={abs/1901.02199}
}

@inproceedings{Bartunov2018FewshotGM,
  title={Few-shot Generative Modelling with Generative Matching Networks},
  author={Sergey Bartunov and Dmitry P. Vetrov},
  booktitle={AISTATS},
  year={2018}
}

@article{Finn2017ModelAgnosticMF,
  title={Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks},
  author={Chelsea Finn and P. Abbeel and Sergey Levine},
  journal={ArXiv},
  year={2017},
  volume={abs/1703.03400}
}

@article{Nichol2018OnFM,
  title={On First-Order Meta-Learning Algorithms},
  author={Alex Nichol and Joshua Achiam and John Schulman},
  journal={ArXiv},
  year={2018},
  volume={abs/1803.02999}
}

@article{Li2017MetaSGDLT,
  title={Meta-SGD: Learning to Learn Quickly for Few Shot Learning},
  author={Zhenguo Li and Fengwei Zhou and Fei Chen and Hang Li},
  journal={ArXiv},
  year={2017},
  volume={abs/1707.09835}
}

@inproceedings{Rajeswaran2019MetaLearningWI,
  title={Meta-Learning with Implicit Gradients},
  author={Aravind Rajeswaran and Chelsea Finn and Sham M. Kakade and Sergey Levine},
  booktitle={NeurIPS},
  year={2019}
}

@inproceedings{
sridhar2022metagan,
title={Meta-{GAN} for Few-Shot Image Generation},
author={Arvind Sridhar},
booktitle={ICLR Workshop on Deep Generative Models for Highly Structured Data},
year={2022},
url={https://openreview.net/forum?id=SE3Gy6E_PWq}
}

@article{Robb2020FewShotAO,
  title={Few-Shot Adaptation of Generative Adversarial Networks},
  author={Esther Robb and Wen-Sheng Chu and Abhishek Kumar and Jia-Bin Huang},
  journal={ArXiv},
  year={2020},
  volume={abs/2010.11943}
}

@article{Liang2020DAWSONAD,
  title={DAWSON: A Domain Adaptive Few Shot Generation Framework},
  author={Weixin Liang and Zixuan Liu and Can Liu},
  journal={ArXiv},
  year={2020},
  volume={abs/2001.00576}
}

@article{Edwards2017TowardsAN,
  title={Towards a Neural Statistician},
  author={Harrison Edwards and Amos J. Storkey},
  journal={ArXiv},
  year={2017},
  volume={abs/1606.02185}
}

@article{CHENG2022106719,
title = {Transfer prior knowledge from surrogate modelling: A meta-learning approach},
journal = {Computers \& Structures},
volume = {260},
pages = {106719},
year = {2022},
issn = {0045-7949},
doi = {https://doi.org/10.1016/j.compstruc.2021.106719},
url = {https://www.sciencedirect.com/science/article/pii/S0045794921002418},
author = {Minghui Cheng and Chao Dang and Dan M. Frangopol and Michael Beer and Xian-Xun Yuan},
}

@article{Liu2022ANM,
  title={A novel meta-learning initialization method for physics-informed neural networks},
  author={Xu Liu and Xiaoya Zhang and Wei Peng and Weien Zhou and Wen Yao},
  journal={Neural Comput. Appl.},
  year={2022},
  volume={34},
  pages={14511-14534}
}

@article{Chen2022MetaMgNetMM,
  title={Meta-MgNet: Meta Multigrid Networks for Solving Parameterized Partial Differential Equations},
  author={Yuyan Chen and Bin Dong and Jinchao Xu},
  journal={J. Comput. Phys.},
  year={2022},
  volume={455},
  pages={110996}
}

@article{Goswami2022DeepTL,
  title={Deep transfer learning for partial differential equations under conditional shift with DeepONet},
  author={Somdatta Goswami and Katiana Kontolati and Michael D. Shields and George Em Karniadakis},
  journal={ArXiv},
  year={2022},
  volume={abs/2204.09810}
}


@article{CHEN2022110996,
author = {Yuyan Chen and Bin Dong and Jinchao Xu},
doi = {https://doi.org/10.1016/j.jcp.2022.110996},
issn = {0021-9991},
journal = {Journal of Computational Physics},
keywords = {Parameterized PDEs, Multigrid, Deep-learning, MgNet, Meta-learning},
pages = {110996},
title = {Meta-MgNet: Meta multigrid networks for solving parameterized partial differential equations},
url = {https://www.sciencedirect.com/science/article/pii/S0021999122000584},
volume = {455},
year = {2022},
bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0021999122000584},
bdsk-url-2 = {https://doi.org/10.1016/j.jcp.2022.110996}}



@article{xu2022meta,
author = {Liu, Xu and Zhang, Xiaoya and Peng, Wei and Zhou, Weien and Yao, Wen},
date = {2022/09/01},
date-added = {2023-03-26 14:25:44 -0400},
date-modified = {2023-03-26 14:25:44 -0400},
doi = {10.1007/s00521-022-07294-2},
id = {Liu2022},
isbn = {1433-3058},
journal = {Neural Computing and Applications},
number = {17},
pages = {14511--14534},
title = {A novel meta-learning initialization method for physics-informed neural networks},
url = {https://doi.org/10.1007/s00521-022-07294-2},
volume = {34},
year = {2022},
bdsk-url-1 = {https://doi.org/10.1007/s00521-022-07294-2}}


@article{Chakraborty2021TransferLB,
  title={Transfer learning based multi-fidelity physics informed deep neural network},
  author={Souvik Lal Chakraborty},
  journal={J. Comput. Phys.},
  year={2021},
  volume={426},
  pages={109942}
}


@article{doi:10.1080/07362999008809220,
	author = {Denis Talay and Luciano Tubaro},
	doi = {10.1080/07362999008809220},
	eprint = {https://doi.org/10.1080/07362999008809220},
	journal = {Stochastic Analysis and Applications},
	number = {4},
	pages = {483-509},
	publisher = {Taylor & Francis},
	title = {Expansion of the global error for numerical schemes solving stochastic differential equations},
	url = {https://doi.org/10.1080/07362999008809220},
	volume = {8},
	year = {1990},
	bdsk-url-1 = {https://doi.org/10.1080/07362999008809220}}



@article{BallyTalay1995,
	author = {Bally, V. and Talay, D.},
	date = {1996/03/01},
	date-added = {2022-12-16 07:43:28 -0500},
	date-modified = {2022-12-16 07:43:28 -0500},
	doi = {10.1007/BF01303802},
	id = {Bally1996},
	isbn = {1432-2064},
	journal = {Probability Theory and Related Fields},
	number = {1},
	pages = {43--60},
	title = {The law of the Euler scheme for stochastic differential equations},
	url = {https://doi.org/10.1007/BF01303802},
	volume = {104},
	year = {1996},
	bdsk-url-1 = {https://doi.org/10.1007/BF01303802}}

@article{10.1287/opre.1070.0496,
author = {Giles, Michael B.},
title = {Multilevel Monte Carlo Path Simulation},
year = {2008},
issue_date = {May 2008},
publisher = {INFORMS},
address = {Linthicum, MD, USA},
volume = {56},
number = {3},
issn = {0030-364X},
url = {https://doi.org/10.1287/opre.1070.0496},
doi = {10.1287/opre.1070.0496},
journal = {Oper. Res.},
month = {may},
pages = {607–617},
numpages = {11},
keywords = {computational complexity, efficiency, finance, analysis of algorithms, simulation}
}
@article{papamakarios2021normalizing,
  title={Normalizing flows for probabilistic modeling and inference},
  author={Papamakarios, George and Nalisnick, Eric and Rezende, Danilo Jimenez and Mohamed, Shakir and Lakshminarayanan, Balaji},
  journal={The Journal of Machine Learning Research},
  volume={22},
  number={1},
  pages={2617--2680},
  year={2021},
  publisher={JMLRORG}
}

@article{Cheridito2005SecondorderBS,
  title={Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs},
  author={Patrick Cheridito and Halil Mete Soner and Nizar Touzi and Nicolas Victoir},
  journal={Communications on Pure and Applied Mathematics},
  year={2005},
  volume={60}
}

@misc{lqg_hjb,
   author = "{Emanuel Todorov}",
   title = "Linear-Quadratic-Gaussian (LQG) Controllers",
   year = "2014",
   url = "https://homes.cs.washington.edu/~todorov/courses/cseP590/10_LQG.pdf",
   note = "[Online; accessed 1-January-2023]"
 }

@inproceedings{Hawkins2021ValueFE,
  title={Value Function Estimators for Feynman-Kac Forward-Backward SDEs in Stochastic Optimal Control},
  author={Kelsey P. Hawkins and Ali Pakniyat and Panagiotis Tsiotras},
  year={2021}
}
@article{newton1994variance,
  title={Variance reduction for simulated diffusions},
  author={Newton, Nigel J},
  journal={SIAM journal on applied mathematics},
  volume={54},
  number={6},
  pages={1780--1805},
  year={1994},
  publisher={SIAM}
}

@article{sen2018gentle,
  title={A gentle introduction to empirical process theory and applications},
  author={Sen, Bodhisattva},
  journal={Lecture Notes, Columbia University},
  volume={11},
  pages={28--29},
  year={2018}
}


@article{qin2022meta,
  title={Meta-PDE: Learning to Solve PDEs Quickly Without a Mesh},
  author={Qin, Tian and Beatson, Alex and Oktay, Deniz and McGreivy, Nick and Adams, Ryan P},
  journal={arXiv preprint arXiv:2211.01604},
  year={2022}
}


@article{nusken2021interpolating,
  title={Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems},
  author={N{\"u}sken, Nikolas and Richter, Lorenz},
  journal={arXiv preprint arXiv:2112.03749},
  year={2021}
}

@article{glau2022deep,
  title={The deep parametric PDE method and applications to option pricing},
  author={Glau, Kathrin and Wunderlich, Linus},
  journal={Applied Mathematics and Computation},
  volume={432},
  pages={127355},
  year={2022},
  publisher={Elsevier}
}
@article{berner2020numerically,
  title={Numerically solving parametric families of high-dimensional Kolmogorov partial differential equations via deep learning},
  author={Berner, Julius and Dablander, Markus and Grohs, Philipp},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={16615--16627},
  year={2020}
}
@inproceedings{richter2022robust,
  title={Robust SDE-based variational formulations for solving linear PDEs via deep learning},
  author={Richter, Lorenz and Berner, Julius},
  booktitle={International Conference on Machine Learning},
  pages={18649--18666},
  year={2022},
  organization={PMLR}
}



@article{krishnapriyan2021characterizing,
  title={Characterizing possible failure modes in physics-informed neural networks},
  author={Krishnapriyan, Aditi and Gholami, Amir and Zhe, Shandian and Kirby, Robert and Mahoney, Michael W},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={26548--26560},
  year={2021}
}

@article{wang2021understanding,
  title={Understanding and mitigating gradient flow pathologies in physics-informed neural networks},
  author={Wang, Sifan and Teng, Yujun and Perdikaris, Paris},
  journal={SIAM Journal on Scientific Computing},
  volume={43},
  number={5},
  pages={A3055--A3081},
  year={2021},
  publisher={SIAM}
}


@article{raissi2019physics,
  title={Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
  author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George E},
  journal={Journal of Computational physics},
  volume={378},
  pages={686--707},
  year={2019},
  publisher={Elsevier}
}

@article{fahim2011probabilistic,
  title={A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs},
  author={Fahim, Arash and Touzi, Nizar and Warin, Xavier},
  journal={The Annals of Applied Probability},
  pages={1322--1364},
  year={2011},
  publisher={JSTOR}
}

@book{evans2022partial,
  title={Partial differential equations},
  author={Evans, Lawrence C},
  volume={19},
  year={2022},
  publisher={American Mathematical Society}
}

@article{margossian2019review,
  title={A review of automatic differentiation and its efficient implementation},
  author={Margossian, Charles C},
  journal={Wiley interdisciplinary reviews: data mining and knowledge discovery},
  volume={9},
  number={4},
  pages={e1305},
  year={2019},
  publisher={Wiley Online Library}
}



@book{pardoux2014stochastic,
  title={Stochastic differential equations, Backward SDEs, Partial differential equations},
  author={Pardoux, Etienne and R{\^a}șcanu, Aurel},
  volume={69},
  year={2014},
  publisher={Springer}
}


@article{huang2022meta,
  title={Meta-auto-decoder for solving parametric partial differential equations},
  author={Huang, Xiang and Ye, Zhanhong and Liu, Hongsheng and Ji, Shi and Wang, Zidong and Yang, Kang and Li, Yang and Wang, Min and Chu, Haotian and Yu, Fan and others},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={23426--23438},
  year={2022}
}


@article{gupta2021multiwavelet,
  title={Multiwavelet-based operator learning for differential equations},
  author={Gupta, Gaurav and Xiao, Xiongye and Bogdan, Paul},
  journal={Advances in neural information processing systems},
  volume={34},
  pages={24048--24062},
  year={2021}
}

@article{ait2008closed,
  title={Closed-Form Likelihood Expansions for Multivariate Diffusions},
  author={A{\"\i}t-Sahalia, Yacine},
  journal={The Annals of Statistics},
  pages={906--937},
  year={2008},
  publisher={JSTOR}
}

@article{Lu2019LearningNO,
  title={Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators},
  author={Lu Lu and Pengzhan Jin and Guofei Pang and Zhongqiang Zhang and George Em Karniadakis},
  journal={Nature Machine Intelligence},
  year={2019},
  volume={3},
  pages={218 - 229}
}

@article{Li2020FourierNO,
  title={Fourier Neural Operator for Parametric Partial Differential Equations},
  author={Zong-Yi Li and Nikola B. Kovachki and Kamyar Azizzadenesheli and Burigede Liu and Kaushik Bhattacharya and Andrew Stuart and Anima Anandkumar},
  journal={ArXiv},
  year={2020},
  volume={abs/2010.08895}
}

@article{Wang2021LearningTS,
  title={Learning the solution operator of parametric partial differential equations with physics-informed DeepONets},
  author={Sifan Wang and Hanwen Wang and Paris Perdikaris},
  journal={Science Advances},
  year={2021},
  volume={7}
}

@article{Zheng2022FastSO,
  title={Fast Sampling of Diffusion Models via Operator Learning},
  author={Hongkai Zheng and Weili Nie and Arash Vahdat and Kamyar Azizzadenesheli and Anima Anandkumar},
  journal={ArXiv},
  year={2022},
  volume={abs/2211.13449}
}


@article{Tran2021FactorizedFN,
  title={Factorized fourier neural operators},
  author={Tran, Alasdair and Mathews, Alexander and Xie, Lexing and Ong, Cheng Soon},
  journal={arXiv preprint arXiv:2111.13802},
  year={2021}
}

@article{Li2022FourierNO,
  title={Fourier Neural Operator with Learned Deformations for PDEs on General Geometries},
  author={Zong-Yi Li and Daniel Zhengyu Huang and Burigede Liu and Anima Anandkumar},
  journal={ArXiv},
  year={2022},
  volume={abs/2207.05209}
}

@inproceedings{Long2017PDENetLP,
  title={PDE-Net: Learning PDEs from Data},
  author={Zichao Long and Yiping Lu and Xianzhong Ma and Bin Dong},
  booktitle={International Conference on Machine Learning},
  year={2017}
}

@inproceedings{NEURIPS2021_0a9fdbb1,
 author = {Song, Yang and Durkan, Conor and Murray, Iain and Ermon, Stefano},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan},
 pages = {1415--1428},
 publisher = {Curran Associates, Inc.},
 title = {Maximum Likelihood Training of Score-Based Diffusion Models},
 url = {https://proceedings.neurips.cc/paper_files/paper/2021/file/0a9fdbb17feb6ccb7ec405cfb85222c4-Paper.pdf},
 volume = {34},
 year = {2021}
}

@inproceedings{NEURIPS2021_67d96d45,
 author = {Hoogeboom, Emiel and Nielsen, Didrik and Jaini, Priyank and Forr\'{e}, Patrick and Welling, Max},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan},
 pages = {12454--12465},
 publisher = {Curran Associates, Inc.},
 title = {Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions},
 url = {https://proceedings.neurips.cc/paper_files/paper/2021/file/67d96d458abdef21792e6d8e590244e7-Paper.pdf},
 volume = {34},
 year = {2021}
}

@article{Song2020DenoisingDI,
  title={Denoising Diffusion Implicit Models},
  author={Jiaming Song and Chenlin Meng and Stefano Ermon},
  journal={ArXiv},
  year={2020},
  volume={abs/2010.02502}
}

@inproceedings{NEURIPS2021_940392f5,
 author = {De Bortoli, Valentin and Thornton, James and Heng, Jeremy and Doucet, Arnaud},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan},
 pages = {17695--17709},
 publisher = {Curran Associates, Inc.},
 title = {Diffusion Schr\"{o}dinger Bridge with Applications to Score-Based Generative Modeling},
 url = {https://proceedings.neurips.cc/paper_files/paper/2021/file/940392f5f32a7ade1cc201767cf83e31-Paper.pdf},
 volume = {34},
 year = {2021}
}

@article{Berner2022AnOC,
  title={An optimal control perspective on diffusion-based generative modeling},
  author={Julius Berner and Lorenz Richter and Karen Ullrich},
  journal={ArXiv},
  year={2022},
  volume={abs/2211.01364}
}


@InProceedings{pmlr-v139-wang21l,
  title = 	 {Deep Generative Learning via Schr{ö}dinger Bridge},
  author =       {Wang, Gefei and Jiao, Yuling and Xu, Qian and Wang, Yang and Yang, Can},
  booktitle = 	 {Proceedings of the 38th International Conference on Machine Learning},
  pages = 	 {10794--10804},
  year = 	 {2021},
  editor = 	 {Meila, Marina and Zhang, Tong},
  volume = 	 {139},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {18--24 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v139/wang21l/wang21l.pdf},
  url = 	 {https://proceedings.mlr.press/v139/wang21l.html},
}

@article{EXARCHOS2018159,
title = {Stochastic optimal control via forward and backward stochastic differential equations and importance sampling},
journal = {Automatica},
volume = {87},
pages = {159-165},
year = {2018},
issn = {0005-1098},
doi = {https://doi.org/10.1016/j.automatica.2017.09.004},
url = {https://www.sciencedirect.com/science/article/pii/S0005109817304740},
author = {Ioannis Exarchos and Evangelos A. Theodorou},
keywords = {Stochastic control, Forward and backward stochastic differential equations, Importance sampling},
}

@article{bender2010importance,
  title={Importance sampling for backward SDEs},
  author={Bender, Christian and Moseler, Thilo},
  journal={Stochastic Analysis and Applications},
  volume={28},
  number={2},
  pages={226--253},
  year={2010},
  publisher={Taylor \& Francis}
}

@article{Raissi2018ForwardBackwardSN,
  title={Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations},
  author={Maziar Raissi},
  journal={ArXiv},
  year={2018},
  volume={abs/1804.07010}
}

@article{Jackson2022NumericalSO,
  title={Numerical simulations of stochastic inflation using importance sampling},
  author={Joseph H.P. Jackson and Hooshyar Assadullahi and Kazuya Koyama and Vincent Vennin and David Wands},
  journal={Journal of Cosmology and Astroparticle Physics},
  year={2022},
  volume={2022}
}


@article{RICHARD20071385,
	author = {Jean-Francois Richard and Wei Zhang},
	doi = {https://doi.org/10.1016/j.jeconom.2007.02.007},
	issn = {0304-4076},
	journal = {Journal of Econometrics},
	keywords = {Monte Carlo, Importance sampling, Marginalized likelihood, Stochastic volatility, Random effects},
	number = {2},
	pages = {1385-1411},
	title = {Efficient high-dimensional importance sampling},
	url = {https://www.sciencedirect.com/science/article/pii/S0304407607000486},
	volume = {141},
	year = {2007},
	bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0304407607000486},
	bdsk-url-2 = {https://doi.org/10.1016/j.jeconom.2007.02.007}}


@article{bsb2019,
	author = {Li, Xinpeng and Lin, Yiqing and Xu, Weicheng},
	date = {2019/05/17},
	date-added = {2023-05-13 22:11:08 -0600},
	date-modified = {2023-05-13 22:11:08 -0600},
	doi = {10.1186/s13662-019-2135-z},
	id = {Li2019},
	isbn = {1687-1847},
	journal = {Advances in Difference Equations},
	number = {1},
	pages = {193},
	title = {On properties of solutions to Black--Scholes--Barenblatt equations},
	url = {https://doi.org/10.1186/s13662-019-2135-z},
	volume = {2019},
	year = {2019},
	bdsk-url-1 = {https://doi.org/10.1186/s13662-019-2135-z}}

@article{Dinh2014NICENI,
  title={NICE: Non-linear Independent Components Estimation},
  author={Laurent Dinh and David Krueger and Yoshua Bengio},
  journal={CoRR},
  year={2014},
  volume={abs/1410.8516}
}

@article{Dinh2016DensityEU,
  title={Density estimation using Real NVP},
  author={Laurent Dinh and Jascha Narain Sohl-Dickstein and Samy Bengio},
  journal={ArXiv},
  year={2016},
  volume={abs/1605.08803}
}

@article{Stimper2023normflowsAP,
  title={normflows: A PyTorch Package for Normalizing Flows},
  author={Vincent Stimper and David Liu and Andrew Campbell and Vincent Berenz and Lukas Ryll and Bernhard Scholkopf and Jos{\'e} Miguel Hern{\'a}ndez-Lobato},
  journal={ArXiv},
  year={2023},
  volume={abs/2302.12014}
}

@article{Grathwohl2018FFJORDFC,
  title={FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models},
  author={Will Grathwohl and Ricky T. Q. Chen and Jesse Bettencourt and Ilya Sutskever and David Kristjanson Duvenaud},
  journal={ArXiv},
  year={2018},
  volume={abs/1810.01367}
}


@article{doi:10.1080/07362990903546405,
    author = {Christian Bender and Thilo Moseler},
	doi = {10.1080/07362990903546405},
	eprint = {https://doi.org/10.1080/07362990903546405},
	journal = {Stochastic Analysis and Applications},
	number = {2},
	pages = {226-253},
	publisher = {Taylor & Francis},
	title = {Importance Sampling for Backward SDEs},
	url = {https://doi.org/10.1080/07362990903546405},
	volume = {28},
	year = {2010},
	bdsk-url-1 = {https://doi.org/10.1080/07362990903546405}
 }

@misc{zhang2023monte,
      title={Monte Carlo Neural Operator for Learning PDEs via Probabilistic Representation}, 
      author={Rui Zhang and Qi Meng and Rongchan Zhu and Yue Wang and Wenlei Shi and Shihua Zhang and Zhi-Ming Ma and Tie-Yan Liu},
      year={2023},
      eprint={2302.05104},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

@article{E_2017,
	doi = {10.1007/s40304-017-0117-6},
	url = {https://doi.org/10.1007%2Fs40304-017-0117-6},
	year = 2017,
	month = {nov},
	publisher = {Springer Science and Business Media {LLC}},
	volume = {5},
	number = {4},
	pages = {349--380},
	author = {Weinan E and Jiequn Han and Arnulf Jentzen},
	title = {Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations},
	journal = {Communications in Mathematics and Statistics}
}

@article{Hu2023TacklingTC,
  title={Tackling the Curse of Dimensionality with Physics-Informed Neural Networks},
  author={Zheyuan Hu and Khemraj Shukla and George Em Karniadakis and Kenji Kawaguchi},
  journal={ArXiv},
  year={2023},
  volume={abs/2307.12306},
  url={https://api.semanticscholar.org/CorpusID:260125464}
}