MAE Seminar: Deep Learning and Scientific Computing
Verne M. Willaman Professor of Mathematics
Director of the Center for Computational Mathematics and Applications
Penn State University
Zoom Link: https://uci.zoom.us/j/96306794654
Abstract: Deep Learning has found many successful applications in artificial intelligence (AI) for tasks such as image recognition, natural language processing and autonomous driving. In this talk, I will first give an elementary introduction of basic deep learning models and training algorithms from a mathematical viewpoint. In particular, I will relate deep learning with some classic numerical methods such as finite element and multigrid method. Using image classification as an example, I will try to give mathematical explanations why and how some popular deep learning models such as convolutional neural network (CNN) work. Finally, I will use some simple model problems to explain how deep learning can be used in scientific and engineering computing.
Bio: Jinchao Xu is the Verne M. Willaman Professor of Mathematics and director of the Center for Computational Mathematics and Applications at 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 (PDEs) and their applications. His recent research interests also include the mathematical analysis and applications of deep neural networks and related training algorithms. He is known, for example, for the Bramble-Pasciak-Xu preconditioner and the Hiptmair-Xu preconditioner basic multigrid methods for solving PDEs. 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) and the American Association for the Advancement of Science (AAAS).