Time: Monday, June 24th, 2024 , 10:00-11:00
Speaker: Xiaoliang Wan, Professor, Department of Mathematics and CCT at Louisiana State University
Abstract:In this talk we discuss adaptive sampling for physics informed neural networks (PINNs). In contrast to classical numerical methods for the approximation of PDEs, PINNs employ random samples instead of Gauss quadrature points for integral, which introduce a statistical error into the approximate solution. PINNs may not perform well when the statistical error overwhelms the approximation error. This suggests the random samples in the training set should also be optimized, which results in adaptive sampling. We will introduce two adaptive sampling strategies: deep adaptive sampling (DAS) and adversarial adaptive sampling (AAS) to improve the accuracy of PINNs for the approximation of (parametric) PDEs especially when the solution is of low regularity or the dimension is relatively high.