2.3k citations · 9.6k across the 47 of their papers we have counts for
50 papers
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
Jiequn Han, Arnulf Jentzen, Weinan E
High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of t…
Deep Picard Iteration for High-Dimensional Nonlinear PDEs
Jiequn Han, Wei Hu, Jihao Long +1
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies…
Learning Free Terminal Time Optimal Closed-loop Control of Manipulators
Wei Hu, Yue Zhao, Weinan E +2
This paper presents a novel approach to learning free terminal time closed-loop control for robotic manipulation tasks, enabling dynamic adjustment of task duration and control inp…
Improving Gradient Computation for Differentiable Physics Simulation with Contacts
Yaofeng Desmond Zhong, Jiequn Han, Biswadip Dey +1
Differentiable simulation enables gradients to be back-propagated through physics simulations. In this way, one can learn the dynamics and properties of a physics system by gradien…
DeePMD-kit v2: A software package for Deep Potential models
Jinzhe Zeng, Duo Zhang, Denghui Lu +44
DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. T…
Reinforcement Learning with Function Approximation: From Linear to Nonlinear
Jihao Long, Jiequn Han
Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This…
A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problem
Mo Zhou, Jiequn Han, Manas Rachh +1
We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the…
Offline Supervised Learning V.S. Online Direct Policy Optimization: A Comparative Study and A Unified Training Paradigm for Neural Network-Based Optimal Feedback Control
Yue Zhao, Jiequn Han
This work is concerned with solving neural network-based feedback controllers efficiently for optimal control problems. We first conduct a comparative study of two prevalent approa…
Progressive Optimal Path Sampling for Closed-Loop Optimal Control Design with Deep Neural Networks
Xuanxi Zhang, Jihao Long, Wei Hu +2
Closed-loop optimal control design for high-dimensional nonlinear systems has been a long-standing challenge. Traditional methods, such as solving the associated Hamilton-Jacobi-Be…
Pandemic Control, Game Theory and Machine Learning
Yao Xuan, Robert Balkin, Jiequn Han +2
Game theory has been an effective tool in the control of disease spread and in suggesting optimal policies at both individual and area levels. In this AMS Notices article, we focus…
Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?
Yaofeng Desmond Zhong, Jiequn Han, Georgia Olympia Brikis
In recent years, an increasing amount of work has focused on differentiable physics simulation and has produced a set of open source projects such as Tiny Differentiable Simulator,…
Solving Optimal Control Problems of Rigid-Body Dynamics with Collisions Using the Hybrid Minimum Principle
Wei Hu, Jihao Long, Yaohua Zang +2
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states…
Empowering Optimal Control with Machine Learning: A Perspective from Model Predictive Control
Weinan E, Jiequn Han, Jihao Long
Solving complex optimal control problems have confronted computational challenges for a long time. Recent advances in machine learning have provided us with new opportunities to ad…
Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence
Jiequn Han, Ruimeng Hu, Jihao Long
One of the core problems in mean-field control and mean-field games is to solve the corresponding McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). Most…
A Machine Learning Enhanced Algorithm for the Optimal Landing Problem
Yaohua Zang, Jihao Long, Xuanxi Zhang +3
We propose a machine learning enhanced algorithm for solving the optimal landing problem. Using Pontryagin's minimum principle, we derive a two-point boundary value problem for the…
A PDE-free, neural network-based eddy viscosity model coupled with RANS equations
Ruiying Xu, Xu-Hui Zhou, Jiequn Han +2
Most turbulence models used in Reynolds-averaged Navier-Stokes (RANS) simulations are partial differential equations (PDE) that describe the transport of turbulent quantities. Such…
An equivariant neural operator for developing nonlocal tensorial constitutive models
Jiequn Han, Xu-Hui Zhou, Heng Xiao
Developing robust constitutive models is a fundamental and longstanding problem for accelerating the simulation of complicated physics. Machine learning provides promising tools to…
Frame invariance and scalability of neural operators for partial differential equations
Muhammad I. Zafar, Jiequn Han, Xu-Hui Zhou +1
Partial differential equations (PDEs) play a dominant role in the mathematical modeling of many complex dynamical processes. Solving these PDEs often requires prohibitively high co…
Neural-Network Quantum States for Periodic Systems in Continuous Space
Gabriel Pescia, Jiequn Han, Alessandro Lovato +2
We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parameterized in…
DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks
Jiequn Han, Yucheng Yang, Weinan E
An efficient, reliable, and interpretable global solution method, the Deep learning-based algorithm for Heterogeneous Agent Models (DeepHAM), is proposed for solving high dimension…
Perturbational Complexity by Distribution Mismatch: A Systematic Analysis of Reinforcement Learning in Reproducing Kernel Hilbert Space
Jihao Long, Jiequn Han
Most existing theoretical analysis of reinforcement learning (RL) is limited to the tabular setting or linear models due to the difficulty in dealing with function approximation in…
A Class of Dimension-free Metrics for the Convergence of Empirical Measures
Jiequn Han, Ruimeng Hu, Jihao Long
This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is fre…
An Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation
Jihao Long, Jiequn Han, Weinan E
Reinforcement learning (RL) algorithms based on high-dimensional function approximation have achieved tremendous empirical success in large-scale problems with an enormous number o…
Frame-independent vector-cloud neural network for nonlocal constitutive modeling on arbitrary grids
Xu-Hui Zhou, Jiequn Han, Heng Xiao
Constitutive models are widely used for modeling complex systems in science and engineering, where first-principle-based, well-resolved simulations are often prohibitively expensiv…