Speaker: Jinchao Xu, KAUST and Penn State University

Title: "Deep Learning and Scientific Computing"

Abstract: In this talk, I will report several theoretical and numerical studies of deep neural networks in connection with classic algorithms in scientific computing. Topics include approximation properties of neural network functions (especially for high dimensional problems), error estimates for the finite neuron method, convergence analysis of training algorithms, finite elements versus ReLU deep neural networks, multigrid method versus convolutional neural networks, MgNet versus transformer, subspace correction method  versus federated learning.

Bio: Jinchao Xu is Professor of Applied Mathematics and Computational Sciences at King Abdullah University of Science and Technology, Director of KAUST-SRIBD Joint Lab for Scientific Computing and Machine Learning, Verne M. Willaman Professor of Mathematics and Director of the Center for Computational Mathematics and Applications at the Penn State University. His main research interests are in the design, analysis, and application of numerical methods, especially multilevel and adaptive finite element methods, for systems of partial differential equations and problems with direct applications to science and engineering. His other research interests include the mathematical analysis, modeling and applications of deep neural networks. He was an invited speaker at the International Congress for Industrial and Applied Mathematics in 2007 as well as at the International Congress for Mathematicians in 2010. He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM), the American Mathematical Society (AMS), the American Association for the Advancement of Science (AAAS), the European Academy of Sciences (EURASC) and the Academia Europaea.

Host: Prof. Qiang Du