6 papers
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…
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…
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…
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…
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…
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…