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.
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.
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.
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.
A neural network warm-start approach for the inverse acoustic obstacle scattering problem,
Mo Zhou, Jiequn Han, Manas Rachh, Carlos Borges
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]
An equivariant neural operator for developing nonlocal tensorial constitutive models,
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]
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]
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).
[journal]
[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), (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]