Research Interests:

* Shape generation: random sampling of curves and surfaces.

* Scientific Machine Learning: high-dimensional PDEs, FBSDEs, random difference method, time-dependent operator learning.

* Wave scattering: fast multipole method (FMM) in layered media, integral equation methods.

Employment:

Sep. 2021 -- Now, Special Associate Researcher (特任副研究员), Suzhou Institute for Advanced Research, University of Science and Technology of China.

Publications, Preprints:

(* corresponding author; # equal contribution)

(D) Shape sampling: sampling curves without existing shape data

D1. Wenzhong Zhang, Discrete Gaussian Free Field Methods for Random Curve Shape Generation, Comput. Aided Geom. Des., 102469, 2025.

(C) High-dimensional PDEs (d=10000), FBSDEs, random difference method

C2. Wenjun Xu, Wenzhong Zhang*, A deep shotgun method for solving high-dimensional parabolic partial differential equations, J. Sci. Comput. 104 (2), 1-22, 2025.

Cp1. Wei Cai, Shuixin Fang, Wenzhong Zhang, Zhou Tao, Martingale deep learning for very high dimensional quasi-linear partial differential equations and stochastic optimal controls, arXiv: 2408.14395, 2024.

C1. Wenzhong Zhang, Wei Cai*, FBSDE based neural network algorithms for high-dimensional quasilinear parabolic PDEs, J. Comput. Phys. 470, 111557, 2022.

(B) Multi-scale Deep Learning: MscaleDNN, convergence behavior

B2. Bo Wang, Heng Yuan, Lizuo Liu, Wenzhong Zhang, Wei Cai*, On spectral bias reduction of multi-scale neural networks for regression problems, Neural Networks 185, 107179, 2025.

B1. Bo Wang, Wenzhong Zhang, Wei Cai*, Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains, Comm. Comput. Phys. 28, 2139-2157, 2020.

(A) Fast multipole method (FMM) in layered media, convergence analysis, theory of dyadic Green's functions in layer media

Ap1. Heng Yuan#, Bo Wang#, Wenzhong Zhang*, Wei Cai, Fast Multipole Method for Maxwell's Equations in Layered Media, arXiv:2507.18491, 2025.

A8. Chunzhi Xiang, Bo Wang*, Wenzhong Zhang, Wei Cai, Fast multipole method for the Laplace equation in half plane with Robin boundary condition, J. Sci. Comput. 105 (81), 1-29, 2025.

A7. Wenzhong Zhang, Bo Wang*, Wei Cai, Exponential Convergence Theory of the Multipole and Local Expansions for the 3-D Laplace Equation in Layered Media, Annal. Appl. Math. 39 (2), 99-148, 2023.

A6. Wenzhong Zhang, Bo Wang, Wei Cai*, A Matrix Basis Formulation for the Dyadic Green's Functions of Maxwell's Equations in Layered Media, SIAM J. Appl. Math 82 (5), 1710-1732, 2022.

A5. Bo Wang, Wenzhong Zhang, Wei Cai*, Fast multipole method for 3-D Poisson-Boltzmann equation in layered electrolyte-dielectric media, J. Comput. Phys. 439, 110379, 2021

A4. Bo Wang, Wenzhong Zhang, Wei Cai*, Fast multipole method for 3-D Laplace equation in layered media, Comput. Phys. Comm. 259, 107645, 2021.

A3. Bo Wang, Duan Chen, Bo Zhang, Wenzhong Zhang, Min Hyung Cho, Wei Cai*, Taylor expansion based fast multipole method for 3-D Helmholtz equations in layered media, J. Comput. Phys. 401, 109008, 2020.

A2. Wenzhong Zhang, Bo Wang, Wei Cai*, Exponential Convergence for Multipole and Local Expansions and Their Translations for Sources in Layered Media: Two-Dimensional Acoustic Wave, SIAM J. Numer. Anal. 58 (3), 1440-1468, 2020.

A1. Bo Wang, Wenzhong Zhang, Wei Cai*, Fast Multipole Method for 3-D Helmholtz Equation in Layered Meda, SIAM J. Sci. Comput. 41 (6), A3954-A3981, 2019.