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 learning for very high dimensional quasi-linear partial differential equations and stochastic optimal controls
Wei Cai, Shuixin Fang, Wenzhong Zhang +1
In this paper, a highly parallel and derivative-free martingale neural network learning method is proposed to solve Hamilton-Jacobi-Bellman (HJB) equations arising from stochastic…
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…