My research draws inspiration from various disciplines of science and is devoted to solving high-dimensional problems arising from 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.
09/2022:
I am giving a tutorial on Deep learning algorithms for high-dimensional partial differential equations in Machine Learning and Its Applications organized by Institute for Mathematical Sciences at NUS.
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.
Solving optimal control of rigid-body dynamics with collisions using the hybrid minimum principle,
Wei Hu, Jihao Long, Yaohua Zang, Weinan E, Jiequn Han,
arXiv preprint, (2022).
[arXiv]
Learning high-dimensional McKean-Vlasov forward-backward stochastic differential equations with general distribution dependence,
Jiequn Han, Ruimeng Hu, Jihao Long,
arXiv preprint, (2022).
[arXiv]
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,
arXiv preprint, (2022).
[arXiv]
VCNN-e: A vector-cloud neural network with equivariance for emulating Reynolds stress transport equations,
Jiequn Han, Xu-Hui Zhou, Heng Xiao,
arXiv preprint, (2022).
[arXiv]
DeepHAM: A global solution method for heterogeneous agent models with aggregate shocks,
Jiequn Han, Yucheng Yang, Weinan E,
arXiv preprint, (2021).
[arXiv]
[SSRN]
[slides]
A class of dimensionality-free metrics for the convergence of empirical measures,
Jiequn Han, Ruimeng Hu, Jihao Long,
arXiv preprint, (2021).
[arXiv]
Perturbed gradient descent with occupation time,
Xin Guo, Jiequn Han, Mahan Tajrobehkar, Wenpin Tang,
arXiv preprint, (2020).
[arXiv]
Publications
Empowering optimal control with machine learning: A perspective from model predictive control,
Weinan E, Jiequn Han, Jihao Long,
25th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2022), in press.
[arXiv]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]