主讲人：周涛 中国科学院数学与系统科学研究院研究员
时间：2025年10月9日15：30
地点：徐汇校区三号楼332室
举办单位：数理学院
主讲人介绍：周涛，中国科学院数学与系统科学研究院研究员。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。2018 年担任国防科工局《核挑战专题》不确定性量化方向首席科学家。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。
内容介绍：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.
