学术报告：2021年 09月17日 09:30-10:30，苏州大学-陈景润

陈景润

单   位

苏州大学

报告时间

2021年9月17日

9:30至10:30

报告地点

腾讯会议号：

551 640 119

报告题目

MIM: A deep mixed residual method for solving high-order partial differential equations

报告摘要

In recent years, a significant amount of attention has been paid to solve partial differential equations (PDEs) by deep learning. For example, deep Galerkin method uses the PDE residual in the least-squares sense as the loss function and a deep neural network (DNN) to approximate the PDE solution. In this work, we propose a deep mixed residual method (MIM) to solve PDEs with high-order derivatives. In MIM, we first rewrite a high-order PDE into a first-order system, very much in the same spirit as local discontinuous Galerkin method and mixed finite element method in classical numerical methods for PDEs. We then use the residual of first-order system in the least-squares sense as the loss function, which is in close connection with least-squares finite element method. Numerous results of MIM with different loss functions and different choice of DNNs are given.

报告人简介

陈景润，苏州大学数学与交叉科学研究中心及数学科学学院教授。主要研究方向为材料性质的多尺度建模、分析、算法与仿真（包括材料力学、材料磁学以及材料电学），以及机器学习求解偏微分方程。主要工作发表在SIAM系列期刊，Math. Comp.，J. Comput. Phys.等学术期刊上。