Jiequn Han (韩劼群) Instructor of Mathematics Department of Mathematics Princeton University 1007 Fine Hall, Washington Road Princeton, NJ 08544 USA Email: jiequnh (at) princeton (dot) edu

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About Me

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

My research draws inspiration from various disciplines of science and is devoted to solving high-dimensional problems arising from scientific computing. In particular, I am interested in large-scale molecular dynamics simulation, quantum many-body problem, high-dimensional stochastic control, numerical methods of partial differential equations. I did a research internship in DeepMind during the summer of 2017, under the mentorship of Thore Graepel.

Here are my CV and some related links: Google Scholar profile, ResearchGate profile.

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News

• 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.

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Publications & Preprints

• A class of dimensionality-free metrics for the convergence of empirical measures,
  Jiequn Han, Ruimeng Hu, Jihao Long,
  arXiv preprint, (2021). [arXiv]

• An L2 analysis of reinforcement learning in high dimensions with kernel and neural network approximation,
  Jihao Long, Jiequn Han, Weinan E,
  arXiv preprint, (2021). [arXiv]

• Frame-independent vector-cloud neural network for nonlocal constitutive modelling on arbitrary grids,
  Xu-Hui Zhou, Jiequn Han, Heng Xiao,
  arXiv preprint, (2021). [arXiv]

• Actor-critic method for high dimensional static Hamilton--Jacobi--Bellman partial differential equations based on neural networks,
  Mo Zhou, Jiequn Han, Jianfeng Lu,
  arXiv preprint, (2021). [arXiv]

• Recurrent neural networks for stochastic control problems with delay,
  Jiequn Han, Ruimeng Hu,
  arXiv preprint, (2021). [arXiv]

• 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,
  arXiv preprint, (2021). [arXiv]

• Learning nonlocal constitutive models with neural networks,
  Xu-Hui Zhou, Jiequn Han, Heng Xiao,
  arXiv preprint, (2020). [arXiv]

• Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning,
  Weinan E, Jiequn Han, Arnulf Jentzen,
  arXiv preprint, (2020). [arXiv] [website]

• Convergence of deep fictitious play for stochastic differential games,
  Jiequn Han, Ruimeng Hu, Jihao Long,
  arXiv preprint, (2020). [arXiv]

• Integrating machine learning with physics-based modeling,
  Weinan E, Jiequn Han, Linfeng Zhang,
  arXiv preprint, (2020). [arXiv]

• Perturbed gradient descent with occupation time,
  Xin Guo, Jiequn Han, Wenpin Tang,
  arXiv preprint, (2020). [arXiv]

• Universal approximation of symmetric and anti-symmetric functions,
  Jiequn Han, Yingzhou Li, Lin Lin, Jianfeng Lu, Jiefu Zhang, Linfeng Zhang,
  arXiv preprint, (2019). [arXiv]

• 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]

• 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 (2021). [journal] [NBER]

• 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]

• 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]

• Deep fictitious play for finding Markovian Nash equilibrium in multi-agent games,
  Jiequn Han, Ruimeng Hu,
  Mathematical and Scientific Machine Learning Conferenc(MSML), PMLR 107:221-245 (2020). [proceedings] [arXiv]

• 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]

• 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]

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

• 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]

• 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]

• 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]

• 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]

• 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]

• 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]

• 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]

• 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]

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

• 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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