1 citations · 1 across the 4 of their papers we have counts for
4 papers
Deep Neural networks for solving high-dimensional parabolic partial differential equations
Wenzhong Zhang, Zheyuan Hu, Wei Cai +1
The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based metho…
Deep random difference method for high-dimensional quasilinear parabolic partial differential equations
Wei Cai, Shuixin Fang, Tao Zhou
Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for aut…
Martingale deep neural network for very high-dimensional stochastic optimal controls
Wei Cai, Shuixin Fang, Wenzhong Zhang +1
We propose a martingale deep learning method for very high-dimensional stochastic optimal control problems (SOCPs) via their associated Hamilton--Jacobi--Bellman equations and the…
SOC-MartNet: A Martingale Neural Network for the Hamilton-Jacobi-Bellman Equation without Explicit inf H in Stochastic Optimal Controls
Wei Cai, Shuixin Fang, Tao Zhou
In this paper, we propose a martingale-based neural network, SOC-MartNet, for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) equations where no explicit expression is neede…