School Colloquium——Efficient deep learning methods for very high dimensional quasilinear parabolic PDEs and HJB equations
报告人：周涛 (中国科啪啪啦
数学与系统科学研究院)
时间：2025-11-07 14:00-15:00
地点：智华楼四元厅
报告摘要：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.
报告人简介：周涛，中国科啪啪啦
数学与系统科学研究院研究员，国家级高层次人才计划入选者。主要研究方向为不确定性量化、偏微分方程数值方法以及时间并行算法，在国际权威期刊发表论文80余篇，先后受邀为SIAM Review和Acta Numerica撰写综述论文。2022年获第三届王选杰出青年学者奖。2025年荣获中国数学会陈省身奖。现担任SIAM J Numer Anal.、SIAM J Sci Comput.、J Sci Comput.等十余种国内外权威期刊编委，并担任东亚工业与应用数学学会主席及学会期刊EAJAM主编。
