数学大讲堂

Abstract

Deep learning has recently emerged as a prominent approach for numerically solving partial differential equations. This report will discuss several key challenges in deep learning-based PDE methods, including boundary condition handling, spatial-temporal sampling strategies, and high-dimensional non-convex optimization. It will also explore the feasibility of applying deep learning to operator learning and uncertainty quantification research, and summarize recent advances in this rapidly evolving field.

Biography

Professor Tao Tang is an Academician of the Chinese Academy of Sciences, an Academician of Academia Europaea, and an Academician of The World Academy of Sciences (TWAS). He is currently the President of Guangzhou Nanfang University and Vice President of the Chinese Mathematical Society. Professor Tang's main research interests lie in computational mathematics. His work on high-accuracy algorithms for partial differential equations and computational fluid dynamics has had a profound international impact. He was an invited 45-minute speaker at the International Congress of Mathematicians (ICM) and was elected a Fellow of the Society for Industrial and Applied Mathematics (SIAM) in 2012. Professor Tang has received numerous prestigious awards, including the Leslie Fox Prize in Numerical Analysis, the Feng Kang Prize for Scientific Computing, the Natural Science Award of the Ministry of Education of China, and the National Natural Science Award of China.