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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…
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…
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,…
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…
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…
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…
On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis
Zhong Li, Jiequn Han, Weinan E +1
We study the approximation properties and optimization dynamics of recurrent neural networks (RNNs) when applied to learn input-output relationships in temporal data. We consider t…
Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach
Jiequn Han, Jianfeng Lu, Mo Zhou
We propose a new method to solve eigenvalue problems for linear and semilinear second order differential operators in high dimensions based on deep neural networks. The eigenvalue…
Deep Learning Approximation for Stochastic Control Problems
Jiequn Han, Weinan E
Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-di…