ESR-PINNs:Physics-informed neural networks with expansion-shrinkage resampling selection strategies  

作　　者：刘佳楠 侯庆志 魏建国 孙泽玮 Jianan Liu;Qingzhi Hou;Jianguo Wei;Zewei Sun(College of Intelligence and Computing,Tianjin University,Tianjin 300350,China;State Key Laboratory of Hydraulic Engineering Simulation and Safety,Tianjin University,Tianjin 300350,China)

机构地区：[1]College of Intelligence and Computing,Tianjin University,Tianjin 300350,China [2]State Key Laboratory of Hydraulic Engineering Simulation and Safety,Tianjin University,Tianjin 300350,China

出　　处：《Chinese Physics B》2023年第7期337-346,共10页中国物理B（英文版）

基　　金：Project supported by the National Key Research and Development Program of China(Grant No.2020YFC1807905);the National Natural Science Foundation of China(Grant Nos.52079090 and U20A20316);the Basic Research Program of Qinghai Province(Grant No.2022-ZJ-704).

摘　　要：Neural network methods have been widely used in many fields of scientific research with the rapid increase of computing power.The physics-informed neural networks(PINNs)have received much attention as a major breakthrough in solving partial differential equations using neural networks.In this paper,a resampling technique based on the expansion-shrinkage point(ESP)selection strategy is developed to dynamically modify the distribution of training points in accordance with the performance of the neural networks.In this new approach both training sites with slight changes in residual values and training points with large residuals are taken into account.In order to make the distribution of training points more uniform,the concept of continuity is further introduced and incorporated.This method successfully addresses the issue that the neural network becomes ill or even crashes due to the extensive alteration of training point distribution.The effectiveness of the improved physics-informed neural networks with expansion-shrinkage resampling is demonstrated through a series of numerical experiments.

关 键 词：physical informed neural networks RESAMPLING partial differential equation 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程] O241.82[自动化与计算机技术—控制科学与工程]