Solving PDEs by deep neural networks

主讲人：陈景润

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.

主讲人简介：陈景润，中国科学技术大学教授。主要研究方向为材料性质的多尺度建模、分析、算法与仿真，科学计算与机器学习等。工作发表在J. Comput. Phys.、Math. Comp.、Nature Commun.、SIAM系列期刊等学术期刊上。

邀请人：高华东

时间：2022年10月14日（星期五）10:30-12:30