7 papers
Fully nonlinear parabolic equations under a fixed reference diffusion:weighted Hessian estimates and well-posedness
Jihao Long, Zhenhua Zhao
We develop a fixed-reference weighted theory for terminal-value fully nonlinear parabolic equations. A prescribed uniformly elliptic diffusion starting from a point determine…
A Deep Second-Order Stochastic Residual Method for Fully Nonlinear Parabolic PDEs
Zhenhua Zhao, Jihao Long
We introduce the Deep Second-Order Stochastic Residual Method (D2SRM) for high-dimensional, Hessian-dependent fully nonlinear parabolic PDEs. A single scalar space--time network ge…
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 duality framework for analyzing random feature and two-layer neural networks
Hongrui Chen, Jihao Long, Lei Wu
We consider the problem of learning functions within the and Barron spaces, which play crucial roles in understanding random feature models (RFMs), two-layer n…