Solving PDEs by deep neural networks: Three case studies

：陈景润（中国科学技术大学）
：2022-04-27 16:30
：腾讯会议ID：329822168（无密码）

报告人：陈景润（中国科学技术大学）

时  间：4月27日下午16:30

地  点：腾讯会议ID：329822168（无密码）

内容摘要:

Solving partial differential equations (PDEs) by deep neural networks has attracted significant attentions in recent years. In this presentation, I will discuss three pieces of works related to this topic from the perspective of classical numerical analysis: (1) solving high-order PDEs by designing a new model based on the mixed residual formulation; (2) capturing shock waves with random inputs by designing a new model based on the classical shock-capturing scheme; (3) constructing neural networks by using the low-rank structure explicitly. Numerical tests are provided to show the effectiveness of these ideas.

个人简介：

陈景润，中国科学技术大学数学科学学院/苏州高等研究院教授，国家高层次青年人才。主要研究方向为材料性质的多尺度建模、分析、算法与仿真，机器学习与偏微分方程。主要工作发表在J. Comput. Phys.，Math. Comp.，SIAM系列期刊等应用与计算数学期刊以及Nat. Commun.等交叉学科领域期刊上。

 

联系人：邱建贤