Speaker: Zhou Tao, Professor, Academy of Mathematics and Systems Science, CAS

Date: October 16, 2025

Time: 9:00-10:00 am

Location: B924, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

Solving high-dimensional PDEs with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation to compute large Hessian matrices. We propose a deep random difference method (DRDM) that addresses these issues by approximating the convection-diffusion operator using first-order random differences, avoiding explicit Hessian computation. When incorporated into a Galerkin framework, the DRDM eliminates the need for pointwise evaluation of expectations, resulting in very efficient training procedure. Rigorous error estimates for DRDM are presented for linear PDEs. We further extend the approach to the Hamilton-Jacobi-Bellman (HJB) equations in stochastic optimal control. Numerical experiments demonstrate the efficiency of DRDM for solving quasilinear parabolic PDEs and HJB equations in dimensions up to 100000.

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https://www.view.sdu.edu.cn/info/1020/206597.htm