61 citations · 62 across the 7 of their papers we have counts for
11 papers
Time-Invariant Neural Operators with Applications in Solving Time-Dependent PDEs
Zihan Zhou, Wenzhong Zhang, Lizuo Liu
The deep operator network (DeepONet) is one of the basic architectures for learning nonlinear operators with neural networks. However, for operators that describe the dynamic respo…
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…
On the computation of the dyadic Green's functions of Maxwell's equations in layered media
Heng Yuan, Wenzhong Zhang, Bo Wang
In this paper, two formulations for the computation of the dyadic Green's functions of Maxwell's equations in layered media are presented in details. The first formulation derived…
Fast multipole method for the Laplace equation in half plane with Robin boundary condition
Chunzhi Xiang, Bo Wang, Wenzhong Zhang +1
In this paper, we present a fast multipole method (FMM) for solving the two-dimensional Laplace equation in a half-plane with Robin boundary conditions. The method is based on a no…
Fast Multipole Method for Maxwell's Equations in Layered Media
Heng Yuan, Bo Wang, Wenzhong Zhang +1
We present a fast multipole method (FMM) for solving Maxwell's equations in three-dimensional (3-D) layered media, based on the magnetic vector potential under the…
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…