Multi-Scale-Matching neural networks for thin plate bending problem

作     者：Lei Zhang Guowei He Lei Zhang;Guowei He

作者机构：The State Key Laboratory of Nonlinear MechanicsInstitute of MechanicsChinese Academy of SciencesBeijing 100190China School of Engineering ScienceUniversity of Chinese Academy of SciencesBeijing 100049China 

出 版 物：《Theoretical & Applied Mechanics Letters》 (力学快报（英文版）)

年 卷 期：2024年第14卷第1期

页      面：11-15页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 0811[工学-控制科学与工程] 080102[工学-固体力学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foun-dation of China (NSFC) Basic Science Center Program for"Multiscale Problems in Nonlinear Mechanics"(Grant No. 11988102) supported by the National Natural Science Foundation of China (NSFC)(Grant No. 12202451) 

主　　题：Singular perturbation Physics-informed neural networks Boundary layer Machine learning 

摘      要：Physics-informed neural networks are a useful machine learning method for solving differential equations,but encounter challenges in effectively learning thin boundary layers within singular perturbation *** resolve this issue,multi-scale-matching neural networks are proposed to solve the singular perturbation *** by matched asymptotic expansions,the solution is decomposed into inner solutions for small scales and outer solutions for large scales,corresponding to boundary layers and outer regions,***,to conform neural networks,we introduce exponential stretched variables in the boundary layers to avoid semiinfinite region *** results for the thin plate problem validate the proposed method.