Seminar| Institute of Mathematical Sciences
Time：Thursday, March 23th, 2023, 16:00-17:00
Speaker: Jianguo Huang, School of Mathematical Sciences, Shanghai Jiao Tong University
Abstract: Variational and hemivariational inequalities, as a class of important nonlinear problems, are frequently encountered in various scientific and engineering applications. Traditional numerical methods have some limitations for these problems. In this talk, based on our earlier work (Huang-Wang-Yang (20)), we will first devise an Int-Deep method for numerically solving elliptic variational inequalities, which is a combination of the deep learning method and the semi-smooth Newton's method. Later on, we will devise a locally adaptive deep learning method for numerically solving elliptic hemivariational inequalities--- a class of nonconvex and nonsmooth variational problems. A series of numerical experiments are given to show the performance of the proposed methods and the comparison between the previous methods and the traditional methods. This talk is based on some joint work with Yujian Cao (Alibaba), Chunmei Wang (University of Florida) and Haoqin Wang (Shanghai Jiao Tong University).