报告题目：A priori error analysis and greedy training algorithms for neural networks solving PDEs

报 告 人：洪庆国 教授 Missouri University of Science and Technology

报告时间：2023年09月25日 9:00-11:00

报告地点：腾讯会议 660-618-008

报告摘要：We provide an a priori error analysis for methods solving PDEs using neural networks. We show that the resulting constrained optimization problem can be efficiently solved using greedy algorithms, which replaces stochastic gradient descent. Following this, we show that the error arising from discretizing the energy integrals is bounded both in the deterministic case, i.e. when using numerical quadrature, and also in the stochastic case, i.e. when sampling points to approximate the integrals. This innovative greedy algorithm is tested on several benchmark examples to confirm its efficiency and robustness.

报告人简介：Qingguo Hong is a Professor at the Department of Mathematics and Statistics in Missouri University of Science and Technology. He received his Ph.D. in Computational Mathematics from Peking University in 2012. After that, he joined Johann Radon Institute for Computational and Applied Mathematics (RICAM) at Austrian Academy of Sciences as a Research Scientist. He then moved to Faculty of Mathematics at The University of Duisburg-Essen in 2016 working as a Postdoctoral Scholar. Prior to joining Missouri University of Science and Technology, Dr. Hong worked as a Research Professor at The Pennsylvania State University. His main research interest includes numerical analysis, numerical methods for PDEs, and machine learning. He has published papers on journals such as Math. Comp., SIAM J. Numer. Anal., Numer. Math., J. Comput. Physic., Comput. Methods Appl. Mech. Engrg., Math. Models Methods Appl., Science China: Mathematics and so on.