讲座题目：Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning
主讲人：黄建国 教授
主持人：冯芳 博士后
开始时间：2023-10-27 09:30
讲座地址：数学楼102
主办单位：数学科学学院
报告人简介：
黄建国，上海交通大学数学科学学院长聘教授。1986年和1992年分别在复旦大学获学士和博士学位。2006年获教育部新世纪优秀人才称号，2016年荣获上海市育才奖，2017年荣获上海市教学成果奖一等奖（排名第4），2023年获上海交大教书育人奖二等奖，应邀两次在世界华人数学家大会作45分钟邀请报告。主要从事限元方法与应用，快速算法设计与分析和机器学习算法设计与应用方面的研究工作，共发表学术论文超过100篇，部分在计算与应用数学方面的顶级学术刊物如SIAM系列，Math. Comp.和Numer. Math.等发表。先后主持国家自然科学基金面上项目多项，作为核心成员先后参加国家重点研发计划、中科院先导项目等项目多项。现任国内外知名学术刊物《Communications in Nonlinear Science and Numerical Simulation》等编委。
报告内容：
In this talk, we are going to propose and analyze Friedrichs learning as a novel deep learning methodology that can learn the weak solutions of PDEs via a minimax formulation. The name Friedrichs learning is to highlight the close relation between our learning strategy and Friedrichs theory on symmetric systems of PDEs. The weak solution and the test function in the weak formulation are parameterized as deep neural networks in a mesh-free manner, which are alternately updated to approach the optimal solution networks approximating the weak solution and the optimal test function, respectively. Extensive numerical results indicate that our mesh-free Friedrichs learning method can provide reasonably good solutions for a wide range of PDEs defined on regular and irregular domains, where conventional numerical methods such as finite difference methods and finite element methods may be tedious or difficult to be applied, especially for those with discontinuous solutions in high-dimensional problems. The talk is based on a joint work with Fan Chen (Shanghai Jiao Tong University), Chunmei Wang (University of Florida) and Haizhao Yang (University of Maryland College Park).
