61 citations · 83 across the 13 of their papers we have counts for
14 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 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…
On Spectral Bias Reduction of Multi-scale Neural Networks for Regression Problems
Bo Wang, Heng Yuan, Lizuo Liu +2
In this paper, we derive diffusion equation models in the spectral domain for the evolution of training errors of two-layer multi-scale deep neural networks (MscaleDNN) \cite{caixu…
FBSDE based Neural Network Algorithms for High-Dimensional Quasilinear Parabolic PDEs
Wenzhong Zhang, Wei Cai
In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional q…
Multi-scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains
Bo Wang, Wenzhong Zhang, Wei Cai
In this paper, we study a multi-scale deep neural network (MscaleDNN) as a meshless numerical method for computing oscillatory Stokes flows in complex domains. The MscaleDNN employ…
A Matrix Basis Formulation For The Green's Functions Of Maxwell's Equations And The Elastic Wave Equations In Layered Media
Wenzhong Zhang, Bo Wang, Wei Cai
A matrix basis formulation is introduced to represent the 3 x 3 dyadic Green's functions in the frequency domain for the Maxwell's equations and the elastic wave equation in layere…
Exponential convergence for multipole and local expansions and their translations for sources in layered media: three-dimensional Laplace equation
Bo Wang, Wenzhong Zhang, Wei Cai
In this paper, we prove the exponential convergence of the multipole and local expansions, shifting and translation operators used in fast multipole methods (FMMs) for 3-dimensiona…
Fast Multipole Method for 3-D Linearized Poisson-Boltzmann Equation in Layered Media
Bo Wang, Wen Zhong Zhang, Wei Cai
In this paper, we propose a fast multipole method (FMM) for 3-D linearized Poisson-Boltzmann (PB) equation in layered media. The main framework of the algorithm is analogous to the…
Taylor expansion based fast Multipole Methods for 3-D Helmholtz equations in Layered Media
Bo Wanga, Duan Chen, Bo Zhang +3
In this paper, we develop fast multipole methods for 3D Helmholtz kernel in layered media. Two algorithms based on different forms of Taylor expansion of layered media Green's func…
Exponential convergence for multipole and local expansions and their translations for sources in layered media: 2-D acoustic wave
Wenzhong Zhang, Bo Wang, Wei Cai
In this paper, we will first give a derivation of the multipole expansion (ME) and local expansion (LE) for the far field from sources in general 2-D layered media and the multipol…