Beijing Institute of Mathematical Sciences and Applications

Shing Toung Yau

Xiao Pei Jiao

Friday, November 17, 2023 10:00 PM - 10:30 PM

Online

In this talk, we will share several literatures about the explanation of training dynamics of Physics-informed neural network. Especially, as a uniform framework, neural tangent kernel demonstrates the dynamical behavior when width of NN goes to infinity in the single layer setting. NTK illustrates training one-layer NN with infinite width is the same as a kernel regression. As a consequence, NTK will exhibit the training weights of different parts in loss function which will provide the guidance for adaptive algorithm of revised PINN.

Xiaopei Jiao received his bachelor's degree from the Zhiyuan College of Shanghai Jiao Tong University and his Ph.D. from the Department of Mathematical Sciences at Tsinghua University. He subsequently worked as a postdoctoral researcher at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and at the University of Twente in the Netherlands. His current research interests include finite-dimensional filtering theory, Yau-Yau filtering methods, physics-informed neural networks, and bioinformatics. His research focuses primarily on: (1) using geometric tools such as Lie algebras for solving partial differential equations and classifying nonlinear systems; (2) designing novel numerical algorithms based on physics-informed neural networks.