@article{chen2020neural,
  title={Neural spatio-temporal point processes},
  author={Chen, Ricky T. Q. and Amos, Brandon and Nickel, Maximilian},
  journal={arXiv preprint arXiv:2011.04583},
  year={2020}
}

@article{pereira2022decentralized,
  title={Decentralized safe multi-agent stochastic optimal control using deep FBSDEs and ADMM},
  author={Pereira, Marcus A and Saravanos, Augustinos D and So, Oswin and Theodorou, Evangelos A},
  journal={arXiv preprint arXiv:2202.10658},
  year={2022}
}

@inproceedings{neklyudov2023action,
  title={Action matching: Learning stochastic dynamics from samples},
  author={Neklyudov, Kirill and Brekelmans, Rob and Severo, Daniel and Makhzani, Alireza},
  booktitle={International Conference on Machine Learning},
  pages={25858--25889},
  year={2023},
  organization={PMLR}
}

@article{liu2023generalized,
  title={Generalized Schr$\backslash$" odinger Bridge Matching},
  author={Liu, Guan-Horng and Lipman, Yaron and Nickel, Maximilian and Karrer, Brian and Theodorou, Evangelos A and Chen, Ricky T. Q.},
  journal={arXiv preprint arXiv:2310.02233},
  year={2023}
}

@article{bilovs2021neural,
  title={Neural flows: Efficient alternative to neural ODEs},
  author={Bilo{\v{s}}, Marin and Sommer, Johanna and Rangapuram, Syama Sundar and Januschowski, Tim and G{\"u}nnemann, Stephan},
  journal={Advances in neural information processing systems},
  volume={34},
  pages={21325--21337},
  year={2021}
}

@article{zhang2021path,
  title={Path integral sampler: a stochastic control approach for sampling},
  author={Zhang, Qinsheng and Chen, Yongxin},
  journal={arXiv preprint arXiv:2111.15141},
  year={2021}
}

@article{richter2022neural,
	title={Neural conservation laws: A divergence-free perspective},
	author={Richter-Powell, Jack and Lipman, Yaron and Chen, Ricky T. Q.},
	journal={Advances in Neural Information Processing Systems},
	volume={35},
	pages={38075--38088},
	year={2022}
}

@article{kappen2005path,
  title={Path integrals and symmetry breaking for optimal control theory},
  author={Kappen, Hilbert J},
  journal={Journal of statistical mechanics: theory and experiment},
  volume={2005},
  number={11},
  pages={P11011},
  year={2005},
  publisher={IOP Publishing}
}

@article{daniels2010monotone,
  title={Monotone and partially monotone neural networks},
  author={Daniels, Hennie and Velikova, Marina},
  journal={IEEE Transactions on Neural Networks},
  volume={21},
  number={6},
  pages={906--917},
  year={2010},
  publisher={IEEE}
}

@article{sill1997monotonic,
  title={Monotonic networks},
  author={Sill, Joseph},
  journal={Advances in neural information processing systems},
  volume={10},
  year={1997}
}

@article{salimans2017pixelcnnpp,
  title={Pixelcnn++: Improving the pixelcnn with discretized logistic mixture likelihood and other modifications},
  author={Salimans, Tim and Karpathy, Andrej and Chen, Xi and Kingma, Diederik P},
  journal={arXiv preprint arXiv:1701.05517},
  year={2017}
}

@inproceedings{ho2019flowpp,
  title={Flow++: Improving flow-based generative models with variational dequantization and architecture design},
  author={Ho, Jonathan and Chen, Xi and Srinivas, Aravind and Duan, Yan and Abbeel, Pieter},
  booktitle={International conference on machine learning},
  pages={2722--2730},
  year={2019},
  organization={PMLR}
}

@article{kingma2016improved,
  title={Improved variational inference with inverse autoregressive flow},
  author={Kingma, Durk P and Salimans, Tim and Jozefowicz, Rafal and Chen, Xi and Sutskever, Ilya and Welling, Max},
  journal={Advances in neural information processing systems},
  volume={29},
  year={2016}
}

@article{moon2019visualizing,
  title={Visualizing structure and transitions in high-dimensional biological data},
  author={Moon, Kevin R and Van Dijk, David and Wang, Zheng and Gigante, Scott and Burkhardt, Daniel B and Chen, William S and Yim, Kristina and Elzen, Antonia van den and Hirn, Matthew J and Coifman, Ronald R and others},
  journal={Nature biotechnology},
  volume={37},
  number={12},
  pages={1482--1492},
  year={2019},
  publisher={Nature Publishing Group US New York}
}

@article{albergo2022building,
  title={Building normalizing flows with stochastic interpolants},
  author={Albergo, Michael S and Vanden-Eijnden, Eric},
  journal={arXiv preprint arXiv:2209.15571},
  year={2022}
}

@book{villani2021topics,
  title={Topics in optimal transportation},
  author={Villani, C{\'e}dric},
  volume={58},
  year={2021},
  publisher={American Mathematical Soc.}
}

@article{hutchinson1989stochastic,
  title={A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines},
  journal={Communications in Statistics-Simulation and Computation},
  author={Hutchinson, M.F.},
  volume={18},
  number={3},
  pages={1059--1076},
  year={1989},
  publisher={Taylor \& Francis}
}

@misc{ho2020denoisingdiffusionprobabilisticmodels,
      title={Denoising Diffusion Probabilistic Models}, 
      author={Jonathan Ho and Ajay Jain and Pieter Abbeel},
      year={2020},
      eprint={2006.11239},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2006.11239}, 
}

@misc{song2021scorebasedgenerativemodelingstochastic,
      title={Score-Based Generative Modeling through Stochastic Differential Equations}, 
      author={Yang Song and Jascha Sohl-Dickstein and Diederik P. Kingma and Abhishek Kumar and Stefano Ermon and Ben Poole},
      year={2021},
      eprint={2011.13456},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2011.13456}, 
}

@misc{albergo2023stochasticinterpolantsunifyingframework,
      title={Stochastic Interpolants: A Unifying Framework for Flows and Diffusions}, 
      author={Michael S. Albergo and Nicholas M. Boffi and Eric Vanden-Eijnden},
      year={2023},
      eprint={2303.08797},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2303.08797}, 
}

@misc{lipman2023flowmatchinggenerativemodeling,
      title={Flow Matching for Generative Modeling}, 
      author={Yaron Lipman and Ricky T. Q. Chen and Heli Ben-Hamu and Maximilian Nickel and Matt Le},
      year={2023},
      eprint={2210.02747},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2210.02747}, 
}

@misc{ma2024sitexploringflowdiffusionbased,
      title={SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers}, 
      author={Nanye Ma and Mark Goldstein and Michael S. Albergo and Nicholas M. Boffi and Eric Vanden-Eijnden and Saining Xie},
      year={2024},
      eprint={2401.08740},
      archivePrefix={arXiv},
      primaryClass={cs.CV},
      url={https://arxiv.org/abs/2401.08740}, 
}

@misc{chen2024flowmatchinggeneralgeometries,
      title={Flow Matching on General Geometries}, 
      author={Ricky T. Q. Chen and Yaron Lipman},
      year={2024},
      eprint={2302.03660},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2302.03660}, 
}
@misc{liu2024generalizedschrodingerbridgematching,
      title={Generalized Schr\"odinger Bridge Matching}, 
      author={Guan-Horng Liu and Yaron Lipman and Maximilian Nickel and Brian Karrer and Evangelos A. Theodorou and Ricky T. Q. Chen},
      year={2024},
      eprint={2310.02233},
      archivePrefix={arXiv},
      primaryClass={stat.ML},
      url={https://arxiv.org/abs/2310.02233}, 
}

@misc{peyré2020computationaloptimaltransport,
      title={Computational Optimal Transport}, 
      author={Gabriel Peyré and Marco Cuturi},
      year={2020},
      eprint={1803.00567},
      archivePrefix={arXiv},
      primaryClass={stat.ML},
      url={https://arxiv.org/abs/1803.00567}, 
}

@misc{chen2019neuralordinarydifferentialequations,
      title={Neural Ordinary Differential Equations}, 
      author={Ricky T. Q. Chen and Yulia Rubanova and Jesse Bettencourt and David Duvenaud},
      year={2019},
      eprint={1806.07366},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/1806.07366}, 
}

@article{Kobyzev_2021,
   title={Normalizing Flows: An Introduction and Review of Current Methods},
   volume={43},
   ISSN={1939-3539},
   url={http://dx.doi.org/10.1109/TPAMI.2020.2992934},
   DOI={10.1109/tpami.2020.2992934},
   number={11},
   journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
   publisher={Institute of Electrical and Electronics Engineers (IEEE)},
   author={Kobyzev, Ivan and Prince, Simon J.D. and Brubaker, Marcus A.},
   year={2021},
   month=nov, pages={3964–3979} }

@misc{le2023acceleratingmotionplanningoptimal,
      title={Accelerating Motion Planning via Optimal Transport}, 
      author={An T. Le and Georgia Chalvatzaki and Armin Biess and Jan Peters},
      year={2023},
      eprint={2309.15970},
      archivePrefix={arXiv},
      primaryClass={cs.RO},
      url={https://arxiv.org/abs/2309.15970}, 
}

@misc{pereira2022decentralizedsafemultiagentstochastic,
      title={Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM}, 
      author={Marcus A. Pereira and Augustinos D. Saravanos and Oswin So and Evangelos A. Theodorou},
      year={2022},
      eprint={2202.10658},
      archivePrefix={arXiv},
      primaryClass={cs.MA},
      url={https://arxiv.org/abs/2202.10658}, 
}

@inproceedings{li2020scalable,
  title={Scalable gradients for stochastic differential equations},
  author={Li, Xuechen and Wong, Ting-Kam Leonard and Chen, Ricky T. Q. and Duvenaud, David},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={3870--3882},
  year={2020},
  organization={PMLR}
}

@article{grathwohl2018ffjord,
  title={Ffjord: Free-form continuous dynamics for scalable reversible generative models},
  author={Grathwohl, Will and Chen, Ricky T. Q. and Bettencourt, Jesse and Sutskever, Ilya and Duvenaud, David},
  journal={arXiv preprint arXiv:1810.01367},
  year={2018}
}

@article{chen2020learning,
  title={Learning neural event functions for ordinary differential equations},
  author={Chen, Ricky T. Q. and Amos, Brandon and Nickel, Maximilian},
  journal={International Conference on Learning Representations},
  year={2021}
}

@article{karniadakis2021physics,
  title={Physics-informed machine learning},
  author={Karniadakis, George Em and Kevrekidis, Ioannis G and Lu, Lu and Perdikaris, Paris and Wang, Sifan and Yang, Liu},
  journal={Nature Reviews Physics},
  volume={3},
  number={6},
  pages={422--440},
  year={2021},
  publisher={Nature Publishing Group}
}

@article{cuomo2022scientific,
  title={Scientific machine learning through physics--informed neural networks: Where we are and what’s next},
  author={Cuomo, Salvatore and Di Cola, Vincenzo Schiano and Giampaolo, Fabio and Rozza, Gianluigi and Raissi, Maziar and Piccialli, Francesco},
  journal={Journal of Scientific Computing},
  volume={92},
  number={3},
  pages={88},
  year={2022},
  publisher={Springer}
}

@article{wang2023scientific,
  title={Scientific discovery in the age of artificial intelligence},
  author={Wang, Hanchen and Fu, Tianfan and Du, Yuanqi and Gao, Wenhao and Huang, Kexin and Liu, Ziming and Chandak, Payal and Liu, Shengchao and Van Katwyk, Peter and Deac, Andreea and others},
  journal={Nature},
  volume={620},
  number={7972},
  pages={47--60},
  year={2023},
  publisher={Nature Publishing Group UK London}
}

@article{koshizuka2022neural,
  title={Neural Lagrangian Schr$\backslash$" odinger Bridge: Diffusion Modeling for Population Dynamics},
  author={Koshizuka, Takeshi and Sato, Issei},
  journal={International Conference on Learning Representations},
  year={2023}
}

@article{chen2019residual,
  title={Residual flows for invertible generative modeling},
  author={Chen, Ricky T. Q. and Behrmann, Jens and Duvenaud, David K and Jacobsen, J{\"o}rn-Henrik},
  journal={Advances in Neural Information Processing Systems},
  volume={32},
  year={2019}
}

@article{rubanova2019latent,
  title={Latent ordinary differential equations for irregularly-sampled time series},
  author={Rubanova, Yulia and Chen, Ricky T. Q. and Duvenaud, David K},
  journal={Advances in neural information processing systems},
  volume={32},
  year={2019}
}

@article{neklyudov2023computational,
  title={A computational framework for solving Wasserstein Lagrangian flows},
  author={Neklyudov, Kirill and Brekelmans, Rob and Tong, Alexander and Atanackovic, Lazar and Liu, Qiang and Makhzani, Alireza},
  journal={arXiv preprint arXiv:2310.10649},
  year={2023}
}

@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={Journal of Machine Learning Research},
  volume={22},
  number={57},
  pages={1--64},
  year={2021}
}

@article{tancik2020fourfeat,
    title={Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains},
    author={Matthew Tancik and Pratul P. Srinivasan and Ben Mildenhall and Sara Fridovich-Keil and Nithin Raghavan and Utkarsh Singhal and Ravi Ramamoorthi and Jonathan T. Barron and Ren Ng},
    journal={NeurIPS},
    year={2020}
}

@inproceedings{germain2015made,
  title={Made: Masked autoencoder for distribution estimation},
  author={Germain, Mathieu and Gregor, Karol and Murray, Iain and Larochelle, Hugo},
  booktitle={International conference on machine learning},
  pages={881--889},
  year={2015},
  organization={PMLR}
}

@article{kingma2014adam,
  title={Adam: A method for stochastic optimization},
  author={Kingma, Diederik P},
  journal={arXiv preprint arXiv:1412.6980},
  year={2014}
}

@misc{mortensen1989stochastic,
  title={Stochastic Optimal Control: Theory and Application (Robert F. Stengel)},
  author={Mortensen, Richard E},
  year={1989},
  publisher={Society for Industrial and Applied Mathematics}
}

@book{fleming2012deterministic,
  title={Deterministic and stochastic optimal control},
  author={Fleming, Wendell H and Rishel, Raymond W},
  volume={1},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@misc{holdijk2023stochasticoptimalcontrolcollective,
      title={Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Paths}, 
      author={Lars Holdijk and Yuanqi Du and Ferry Hooft and Priyank Jaini and Bernd Ensing and Max Welling},
      year={2023},
      eprint={2207.02149},
      archivePrefix={arXiv},
      primaryClass={q-bio.BM},
      url={https://arxiv.org/abs/2207.02149}, 
}

@article{hartmann2013characterization,
  title={Characterization of rare events in molecular dynamics},
  author={Hartmann, Carsten and Banisch, Ralf and Sarich, Marco and Badowski, Tomasz and Sch{\"u}tte, Christof},
  journal={Entropy},
  volume={16},
  number={1},
  pages={350--376},
  year={2013},
  publisher={Molecular Diversity Preservation International (MDPI)}
}

@Article{HartmannCarsten,
AUTHOR = {Hartmann, Carsten and Richter, Lorenz and Schütte, Christof and Zhang, Wei},
TITLE = {Variational Characterization of Free Energy: Theory and Algorithms},
JOURNAL = {Entropy},
VOLUME = {19},
YEAR = {2017},
NUMBER = {11},
ARTICLE-NUMBER = {626},
URL = {https://www.mdpi.com/1099-4300/19/11/626},
ISSN = {1099-4300},
ABSTRACT = {The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the different variational formulations for designing efficient stochastic optimization and nonequilibrium simulation algorithms for computing free energies are discussed and illustrated.},
DOI = {10.3390/e19110626}
}

@book{pham2009continuous,
  title={Continuous-time stochastic control and optimization with financial applications},
  author={Pham, Huy{\^e}n},
  volume={61},
  year={2009},
  publisher={Springer Science \& Business Media}
}

@article{FLEMING2004979,
title = {Stochastic optimal control, international finance and debt},
journal = {Journal of Banking \& Finance},
volume = {28},
number = {5},
pages = {979-996},
year = {2004},
issn = {0378-4266},
doi = {https://doi.org/10.1016/S0378-4266(03)00138-9},
url = {https://www.sciencedirect.com/science/article/pii/S0378426603001389},
author = {Wendell H Fleming and Jerome L Stein},
keywords = {Stochastic optimal control, Debt, International finance, Vulnerability to external shocks, Sustainable current account deficits},
abstract = {We use stochastic optimal control-dynamic programming (DP) to derive the optimal debt/net worth, consumption/net worth, current account/net worth, and endogenous growth rate in an economy – which could be a country, region or sector within a country. Unlike the literature that uses an intertemporal budget constraint or the Maximum Principle, the DP approach does not require perfect foresight or certainty equivalence. Our results are generalizations of the Merton model, and are explained graphically within a mean–variance context. Two examples are provided to illustrate the usefulness of our technique in predicting debt crises.}
}

@article{theodorou2011iterative,
  title={An iterative path integral stochastic optimal control approach for learning robotic tasks},
  author={Theodorou, Evangelos and Stulp, Freek and Buchli, Jonas and Schaal, Stefan},
  journal={IFAC Proceedings Volumes},
  volume={44},
  number={1},
  pages={11594--11601},
  year={2011},
  publisher={Elsevier}
}


@misc{zhang2022pathintegralsamplerstochastic,
      title={Path Integral Sampler: a stochastic control approach for sampling}, 
      author={Qinsheng Zhang and Yongxin Chen},
      year={2022},
      eprint={2111.15141},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2111.15141}, 
}

@article{pavlov2018narrow,
  title={Narrow-linewidth lasing and soliton Kerr microcombs with ordinary laser diodes},
  author={Pavlov, NG and Koptyaev, S and Lihachev, GV and Voloshin, AS and Gorodnitskiy, AS and Ryabko, MV and Polonsky, SV and Gorodetsky, ML},
  journal={Nature Photonics},
  volume={12},
  number={11},
  pages={694--698},
  year={2018},
  publisher={Nature Publishing Group UK London}
}

@article{aghion1990model,
  title={A model of growth through creative destruction},
  author={Aghion, P},
  year={1990},
  publisher={JSTOR}
}

@book{bensoussan2013mean,
  title={Mean field games and mean field type control theory},
  author={Bensoussan, Alain and Frehse, Jens and Yam, Phillip and others},
  volume={101},
  year={2013},
  publisher={Springer}
}

@inproceedings{onken2021ot,
  title={Ot-flow: Fast and accurate continuous normalizing flows via optimal transport},
  author={Onken, Derek and Fung, Samy Wu and Li, Xingjian and Ruthotto, Lars},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={35},
  number={10},
  pages={9223--9232},
  year={2021}
}

