Solve PDEs by neural network

Speaker:    Zhi-Qin John Xu, Shanghai Jiao Tong University

Time:         09:00-10:00 , Mar.18

Location:   Tencent Meeting

    会议号：934-354-161

    会议链接：https://meeting.tencent.com/dm/nnAjbWei0BJt

Host:         Qifeng Liao

Abstract:

In this talk, I would discuss two approaches for solving PDEs by neural networks. The first one is to parameterize the solution by a network. In this approach, neural network suffers from a high-frequency curse, pointed by the frequency principle, i.e., neural network learns data from low to high frequency. To overcome the high-frequency curse, a multi-scale neural network is proposed and verified. The second approach is to express the solution by the form of the Green function and parameterize the Green function by a network. We propose a model-operator-data framework. In this approach, the MOD-Net solves a family of PDEs rather than a specific one and is much more efficient than original neural operator because few expensive labels are required, which are computed on coarse grid points with cheap computation cost and significantly improves the model accuracy.

Bio:

Zhi-Qin John Xu is an associate professor at Shanghai Jiao Tong University (SJTU). Zhi-Qin obtain B.S. in Physics (2012) and a Ph.D. degree in Mathematics (2016) from SJTU. Before joining SJTU, Zhi-Qin worked as a postdoc at NYUAD and Courant Institute from 2016 to 2019. He published papers on Journal of Machine Learning Research, AAAI, NeurIPS, Communications in Computational Physics，European Journal of Neuroscience和Communications in Mathematical Sciences etc.