Jiequn Han (韩劼群) Research Scientist Center for Computational Mathematics Flatiron Institute 162 5th Avenue New York, NY 10010 Email: jhan (at) flatironinstitute (dot) org

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About Me

I am a Research Scientist at the Center for Computational Mathematics, Flatiron Institute. Previously, I worked as an Instructor of Mathematics at the Department of Mathematics, Princeton University. I obtained my Ph.D. degree in applied mathematics from the Program in Applied and Computational Mathematics (PACM), Princeton University in June 2018, advised by Prof. Weinan E. Before that, I received my Bachelor degree from the School of Mathematical Sciences, Peking University in July 2013.

I conduct research on machine learning for science, drawing inspiration from various scientific disciplines and focusing on solving high-dimensional problems in scientific computing. My current research interests mainly focus on solving high-dimensional partial differential equations and machine learning based-multiscale modeling. I did a research internship in DeepMind during the summer of 2017, under the mentorship of Thore Graepel.

Here are my CV and some links: Google Scholar profile, ResearchGate profile, Twitter, Maching Learning in CCM.

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News

• 11/2024: Our paper Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning received the IOP Publishing Top Cited Paper Award North America.

• 10/2024: Two papers (Stochastic optimal control matching and Provable posterior sampling with denoising oracles through tilted transport) are accepted to NeurIPS 2024.

• 09/2024: We have a new preprint Deep Picard iteration for high-dimensional nonlinear PDEs, achieving state-of-the-art results in solving high-dimensional PDEs.

• 09/2024: I am giving an invited talk at the computational and applied mathematics colloquium at The Pennsylvania State University.

• 08/2024: I am giving an invited talk at Workshop on Data-driven PDE-based inverse problem.

• 07/2024: Our paper Solving high-dimensional partial differential equations using deep learning received the Frontiers of Science Award in the field of scientific computing at the International Congress of Basic Science (ICBS).

• 07/2024: I am giving an invited talk at the Fourth Symposium on Machine Learning and Dynamical Systems.

• 06/2024: I am giving an invited talk at the Program on Scientific Machine Learning for Simulation and Inverse Modelling at KTH.

• 02/2024: I am giving an invited talk at the Brin MRS Workshop on Scientific Machine Learning: Theory and Algorithms.

• 02/2024: I am giving an invited talk at the scientific computing and numerics seminar at Cornell University.

• 01/2024: I am giving an invited talk at IMS Young Mathematical Scientists Forum — Applied Mathematics.

• 10/2023: Our paper Learning High-Dimensional McKean–Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence (with released code) is accepted to SIAM Journal on Numerical Analysis.

• 10/2023: I am giving an invited talk at the applied mathematics colloquium at Columbia University.

• 10/2023: I am giving an invited talk at the applied math and analysis seminar at Duke University.

• 08/2023: I co-organized (with Qianxiao Li and Xiang Zhou) the minisymposium on the intersection of machine learning, dynamical systems and control at ICIAM 2023 Tokyo. Details can be found here.

• 07/2023: I am giving an invited talk Designing High-Dimensional Closed-Loop Optimal Control Using Deep Neural Networks in New Frontiers in Learning, Control, and Dynamical Systems, ICML 2023.

• 07/2023: Our paper A neural network warm-start approach for the inverse acoustic obstacle scattering problem (with released code) is accepted to Journal of Computational Physics.

• 06/2023: I am giving an invited talk in CBMS Conference: Deep Learning and Numerical PDEs.

• 06/2023: I am giving an invited talk in 2023 Foundations of Computational Mathematics, Workshop on Stochastic Computation.

• 05/2023: I am giving an invited talk in 2023 MATH+X Symposium on Dynamos Planetary, Exploration and General Relativity, Inverse Problems and Machine Learning.

• 05/2023: I am giving an invited talk in 18th Annual Conference on Frontiers in Applied and Computational Mathematics.

• 05/2023: I am giving an invited talk in Inaugural Center for Approximation and Mathematical Data Analytics (CAMDA) Conference.

• 05/2023: I am giving an invited talk Initial value problem enhanced sampling for closed-Loop optimal control design with deep neural networks (slides) in 4th AFOSR Monterey Workshop on Computational Nonlinear Control.

• 05/2023: Our paper An equivariant neural operator for developing nonlocal tensorial constitutive models is accepted to Journal of Computational Physics. See dataset description on NASA Turbulence Modeling Resource.

• 04/2023: I am giving an invited talk in The Hong Kong - Singapore Joint Seminar Series in Financial Mathematics/Engineering.

• 03/2023: Our paper Improving gradient computation for differentiable physics simulation with contacts is accepted to L4DC 2023. See this enlightening blog post with animation.

• 11/2022: Our book chapter A dynamical systems and optimal control approach to deep learning is out in the recent printed book Mathematical Aspects of Deep Learning.

• 11/2022: Our article Pandemic control, game theory, and machine learning is published on Notices of the American Mathematical Society as a feature article.

• 09/2022: I am giving a tutorial on Deep learning algorithms for high-dimensional partial differential equations (slides) in Machine Learning and Its Applications organized by Institute for Mathematical Sciences at NUS.

• 09/2022: I am giving an invited talk in Conference on Frontiers in Machine Learning and Economics: Methods and Applications organized by Federal Reserve Bank of Philadelphia.

• 07/2022: I am giving an invited talk Developing reduced-order PDEs with machine learning-based closure models (slides) in 2nd AI for Science Workshop, ICML 2022.

• 05/2022: Our paper Neural-network quantum states for periodic systems in continuous space is published on Physical Review Research.

• 03/2022: More algorithms for high-dimensional PDEs are updated on deeppde.org. Suggestions and contributions are welcome.

• 01/2022: I am serving as a managing editor of a new journal Journal of Machine Learning (JML). Welcome to submit papers to JML.

• 12/2021: Our working paper DeepHAM: A global solution method for heterogeneous agent models with aggregate shocks is released.

• 12/2021: Our paper Actor-critic method for high dimensional static Hamilton–Jacobi–Bellman partial differential equations based on neural networks is published on SIAM Journal on Scientific Computing.

• 07/2021: Our survey paper Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning is published on Nonlinearity.

• 07/2021: Our survey paper Machine-learning-assisted modeling is published on Physics Today.

• 02/2021: Our paper Income and wealth distribution in macroeconomics: A continuous-time approach is published on The Review of Economic Studies.

• 01/2021: Our paper On the curse of memory in recurrent neural networks: approximation and optimization analysis is accepted to ICLR 2021.

• 07/2020: I co-organized (with Qi Gong and Wei Kang) the minisymposium on the intersection of optimal control and machine learning at the SIAM annual meeting. Details can be found here.

• 12/2019: Deep BSDE solver is updated to support TensorFlow 2.0.

Show More

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Preprints

1. Deep Picard iteration for high-dimensional nonlinear PDEs,
   Jiequn Han, Wei Hu, Jihao Long, Yue Zhao,
   arXiv preprint, (2024). [arXiv]

2. Neural operator-based super-fidelity: A warm-start approach for accelerating steady-state simulations,
   Xu-Hui Zhou, Jiequn Han, Muhammad I. Zafar, Christopher J. Roy, Heng Xiao,
   arXiv preprint, (2023). [arXiv]

3. Learning free terminal time optimal closed-loop control of manipulators,
   Wei Hu, Yue Zhao, Weinan E, Jiequn Han, Jihao Long,
   arXiv preprint, (2023). [arXiv] [webpage]

4. Initial value problem enhanced sampling for closed-loop optimal control design with deep neural networks,
   Xuanxi Zhang, Jihao Long, Wei Hu, Weinan E, Jiequn Han,
   arXiv preprint, (2022). [arXiv]

5. DeepHAM: A global solution method for heterogeneous agent models with aggregate shocks,
   Jiequn Han, Yucheng Yang, Weinan E,
   arXiv preprint, (2021). [arXiv] [SSRN] [slides]

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Publications

1. Posterior sampling with denoising oracles via tilted transport,
   Joan Bruna, Jiequn Han,
   accepted to Conference on Neural Information Processing Systems (NeurIPS), (2024). [arXiv] [slides] [poster]

2. Stochastic optimal control matching,
   Carles Domingo-Enrich, Jiequn Han, Brandon Amos, Joan Bruna, Ricky T. Q. Chen,
   accepted to Conference on Neural Information Processing Systems (NeurIPS), (2024). [arXiv] [code]

3. Offline supervised learning vs. online direct policy optimization: A comparative study and a unified training paradigm for neural network-based optimal feedback control,
   Yue Zhao, Jiequn Han,
   Physica D: Nonlinear Phenomena, 462, 134130 (2024). [journal] [arXiv] [code]

4. Escaping saddle points efficiently with occupation-time-adapted perturbations,
   Xin Guo, Jiequn Han, Mahan Tajrobehkar, Wenpin Tang,
   Journal of Computational Mathematics and Data Science, 10, 100090 (2024). [journal] [arXiv]

5. Learning high-dimensional McKean-Vlasov forward-backward stochastic differential equations with general distribution dependence,
   Jiequn Han, Ruimeng Hu, Jihao Long,
   SIAM Journal on Numerical Analysis, 62(1), 1–24 (2024). [journal] [arXiv] [code]

6. Deep reinforcement learning in finite-horizon to explore the most probable transition pathway,
   Jin Guo, Ting Gao, Peng Zhang, Jiequn Han, Jinqiao Duan,
   Physica D: Nonlinear Phenomena, 458, 133955 (2024). [journal]

7. A class of dimensionality-free metrics for the convergence of empirical measures,
   Jiequn Han, Ruimeng Hu, Jihao Long,
   Stochastic Processes and their Applications, 164, 242–287 (2023). [journal] [arXiv]

8. DeePMD-kit v2: A software package for Deep Potential models,
   Jinzhe Zeng, Duo Zhang, and 45 others, including Jiequn Han,
   Journal of Chemical Physics, 159, 054801 (2023). [journal] [arXiv] [code]

9. Reinforcement learning with function approximation: from linear to nonlinear,
   Jihao Long, Jiequn Han,
   Journal of Machine Learning, 2(3), 161–193 (2023). [journal] [arXiv]

10. A neural network warm-start approach for the inverse acoustic obstacle scattering problem,
    Mo Zhou, Jiequn Han, Manas Rachh, Carlos Borges,
    Journal of Computational Physics, 490, 112341 (2023). [journal] [arXiv] [code]

11. Improving gradient computation for differentiable physics simulation with contacts,
    Yaofeng Desmond Zhong, Jiequn Han, Biswadip Dey, Georgia Olympia Brikis,
    Learning for Dynamics and Control Conference (L4DC), (2023). [proceedings] [arXiv] [blog] [code]

12. An equivariant neural operator for developing nonlocal tensorial constitutive models,
    Jiequn Han, Xu-Hui Zhou, Heng Xiao,
    Journal of Computational Physics, 488, 112243 (2023). [journal] [arXiv] [post on NASA TMR]

13. Dynamical systems and optimal control approach to deep learning,
    Weinan E, Jiequn Han, Qianxiao Li,
    Mathematical Aspects of Deep Learning, Cambridge University Press, 422–438 (2022). [book chapter]

14. A PDE-free, neural network-based eddy viscosity model coupled with RANS equations,
    Ruiying Xu, Xu-Hui Zhou, Jiequn Han, Richard P. Dwight, Heng Xiao,
    International Journal of Heat and Fluid Flow, 98, 109051 (2022). [journal] [arXiv]

15. Empowering optimal control with machine learning: A perspective from model predictive control,
    Weinan E, Jiequn Han, Jihao Long,
    International Symposium on Mathematical Theory of Networks and Systems (MTNS), (2022). [journal] [arXiv]

16. Pandemic control, game theory and machine learning,
    Yao Xuan, Robert Balkin, Jiequn Han, Ruimeng Hu, Hector D Ceniceros,
    Notices of the American Mathematical Society, 69(11), 1878–1887 (2022). [journal] [arXiv]

17. A machine learning enhanced algorithm for the optimal landing problem,
    Yaohua Zang, Jihao Long, Xuanxi Zhang, Wei Hu, Weinan E, Jiequn Han
    Mathematical and Scientific Machine Learning Conference (MSML), (2022). [proceedings] [arXiv]

18. Frame invariance and scalability of neural operators for partial differential equations,
    Muhammad I. Zafar, Jiequn Han, Xu-Hui Zhou, Heng Xiao,
    Communications in Computational Physics, 32, 336–363 (2022). [journal] [arXiv]

19. Neural-network quantum states for periodic systems in continuous space,
    Gabriel Pescia, Jiequn Han, Alessandro Lovato, Jianfeng Lu, Giuseppe Carleo,
    Physical Review Research, 4, 023138 (2022). [journal] [arXiv]

20. Convergence of deep fictitious play for stochastic differential games,
    Jiequn Han, Ruimeng Hu, Jihao Long,
    Frontiers of Mathematical Finance, 1(2), 287–319 (2022). [journal] [arXiv]

21. Perturbational complexity by distribution mismatch: A systematic analysis of reinforcement learning in reproducing kernel Hilbert space,
    Jihao Long, Jiequn Han,
    Journal of Machine Learning, 1(1), 1–37 (2022). [journal] [arXiv] [slides]

22. Universal approximation of symmetric and anti-symmetric functions,
    Jiequn Han, Yingzhou Li, Lin Lin, Jianfeng Lu, Jiefu Zhang, Linfeng Zhang,
    Communications in Mathematical Sciences, 20(5), 1397–1408 (2022). [journal] [arXiv]

23. An L2 analysis of reinforcement learning in high dimensions with kernel and neural network approximation,
    Jihao Long, Jiequn Han, Weinan E,
    CSIAM Transactions on Applied Mathematics, 3(2), 191–220 (2002). [journal] [arXiv]

24. Approximation and optimization theory for linear continuous-time recurrent neural networks,
    Zhong Li, Jiequn Han, Weinan E, Qianxiao Li,
    Journal of Machine Learning Research, 23(42), 1–85 (2022). [journal]

25. Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning,
    Weinan E, Jiequn Han, Arnulf Jentzen,
    Nonlinearity, 35(1), 278–310 (2022). [journal] [arXiv] [website]

26. Frame-independent vector-cloud neural network for nonlocal constitutive modelling on arbitrary grids,
    Xu-Hui Zhou, Jiequn Han, Heng Xiao,
    Computer Methods in Applied Mechanics and Engineering, 388, 114211 (2022). [journal] [arXiv] [code]

27. Income and wealth distribution in macroeconomics: A continuous-time approach,
    Yves Achdou, Jiequn Han, Jean-Michel Lasry, Pierre-Louis Lions, Benjamin Moll,
    The Review of Economic Studies, 89(1), 45–86 (2022). [journal] [NBER]

28. Actor-critic method for high dimensional static Hamilton–Jacobi–Bellman partial differential equations based on neural networks,
    Mo Zhou, Jiequn Han, Jianfeng Lu,
    SIAM Journal on Scientific Computing, 43(6), A4043–A4066 (2021). [journal] [arXiv] [code]

29. Optimal policies for a pandemic: A stochastic game approach and a deep learning algorithm,
    Yao Xuan, Robert Balkin, Jiequn Han, Ruimeng Hu, Hector D Ceniceros,
    Mathematical and Scientific Machine Learning Conference (MSML), (2021). [proceedings] [arXiv]

30. Recurrent neural networks for stochastic control problems with delay,
    Jiequn Han, Ruimeng Hu,
    Mathematics of Control, Signals, and Systems, 33, 775–795 (2021). [journal] [arXiv] [code]

31. Global convergence of policy gradient for linear-quadratic mean-field control/game in continuous time,
    Weichen Wang, Jiequn Han, Zhuoran Yang, Zhaoran Wang,
    International Conference on Machine Learning (ICML), (2021). [proceedings] [arXiv]

32. Learning nonlocal constitutive models with neural networks,
    Xu-Hui Zhou, Jiequn Han, Heng Xiao,
    Computer Methods in Applied Mechanics and Engineering, 384, 113927 (2021). [journal] [arXiv] [code]

33. Machine-learning-assisted modeling,
    Weinan E, Jiequn Han, Linfeng Zhang,
    Physics Today, 74, 7, 36 (2021). [journal] [an early and long version on arXiv]

34. On the curse of memory in recurrent neural networks: approximation and optimization analysis,
    Zhong Li, Jiequn Han, Weinan E, Qianxiao Li,
    International Conference on Learning Representations (ICLR), (2021). [OpenReview]

35. Machine learning moment closures for accurate and efficient simulation of polydisperse evaporating sprays,
    James B. Scoggins, Jiequn Han, Marc Massot,
    AIAA Scitech 2021 Forum, 1786 (2021). [proceedings]

36. Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach,
    Jiequn Han, Jianfeng Lu, Mo Zhou,
    Journal of Computational Physics, 423, 109792 (2020). [journal] [arXiv] [code]

37. Deep fictitious play for finding Markovian Nash equilibrium in multi-agent games,
    Jiequn Han, Ruimeng Hu,
    Mathematical and Scientific Machine Learning Conferenc (MSML), (2020). [proceedings] [arXiv]

38. Convergence of the deep BSDE method for coupled FBSDEs,
    Jiequn Han, Jihao Long,
    Probability, Uncertainty and Quantitative Risk, 5(1), 1–33 (2020). [journal] [arXiv]

39. Uniformly accurate machine learning-based hydrodynamic models for kinetic equations,
    Jiequn Han, Chao Ma, Zheng Ma, Weinan E,
    Proceedings of the National Academy of Sciences, 116(44) 21983–21991 (2019). [journal] [arXiv]

40. Solving many-electron Schrödinger equation using deep neural networks,
    Jiequn Han, Linfeng Zhang, Weinan E,
    Journal of Computational Physics, 399, 108929 (2019). [journal] [arXiv]

41. A mean-field optimal control formulation of deep learning,
    Weinan E, Jiequn Han, Qianxiao Li,
    Research in the Mathematical Sciences, 6:10 (2019). [journal] [arXiv]

42. End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems,
    Linfeng Zhang, Jiequn Han, Han Wang, Wissam A. Saidi, Roberto Car, Weinan E,
    Conference on Neural Information Processing Systems (NeurIPS), (2018). [proceedings] [arXiv] [website] [code]

43. Solving high-dimensional partial differential equations using deep learning,
    Jiequn Han, Arnulf Jentzen, Weinan E,
    Proceedings of the National Academy of Sciences, 115(34), 8505–8510 (2018). [journal] [arXiv] [code]

44. DeePCG: constructing coarse-grained models via deep neural networks,
    Linfeng Zhang, Jiequn Han, Han Wang, Roberto Car, Weinan E,
    The Journal of Chemical Physics, 149, 034101 (2018). [journal] [arXiv] [website]

45. DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics,
    Han Wang, Linfeng Zhang, Jiequn Han, Weinan E,
    Computer Physics Communications, 228, 178–184 (2018). [journal] [arXiv] [website] [code]

46. Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics,
    Linfeng Zhang, Han Wang, Jiequn Han, Roberto Car, Weinan E,
    Physical Review Letters 120(10), 143001 (2018). [journal] [arXiv] [website] [code]

47. Deep Potential: a general representation of a many-body potential energy surface,
    Jiequn Han, Linfeng Zhang, Roberto Car, Weinan E,
    Communications in Computational Physics, 23, 629–639 (2018). [journal] [arXiv] [website]

48. Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations,
    Weinan E, Jiequn Han, Arnulf Jentzen,
    Communications in Mathematics and Statistics, 5, 349–380 (2017). [journal] [arXiv] [code]

49. Deep learning approximation for stochastic control problems,
    Jiequn Han, Weinan E,
    Deep Reinforcement Learning Workshop, NIPS (2016). [arXiv]

50. From microscopic theory to macroscopic theory: a systematic study on modeling for liquid crystals,
    Jiequn Han, Yi Luo, Zhifei Zhang, Pingwen Zhang,
    Archive for Rational Mechanics and Analysis, 215, 741–809 (2015). [journal] [arXiv]

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Mentored Students

I'm open to hosting (remote) undergrad/grad visitors. Feel free to reach out if our research interests intersect in any way.

• Nathan Soedjak (Columbia PhD)

• Xu-Hui Zhou (Virginia Tech PhD)

• Xuanxi Zhang (PKU undergrad → Courant PhD)

• Mo Zhou (Duke PhD → UCLA)

• Jihao Long (PKU undergrad → Princeton PhD)

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