Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems  

作　　者：Long WANG Lei ZHANG Guowei HE 

机构地区：[1]The State Key Laboratory of Nonlinear Mechanics,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China [2]School of Engineering Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第9期1467-1480,共14页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China Basic Science Center Program for“Multiscale Problems in Nonlinear Mechanics”(No.11988102);the National Natural Science Foundation of China(No.12202451)。

摘　　要：A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid mechanics.However,it suffers from singularly perturbed boundary-layer problems in which there exist sharp changes caused by a small perturbation parameter multiplying the highest-order derivatives.In this paper,we introduce Chien's composite expansion method into PINNs,and propose a novel architecture for the PINNs,namely,the Chien-PINN(C-PINN)method.This novel PINN method is validated by singularly perturbed differential equations,and successfully solves the wellknown thin plate bending problems.In particular,no cumbersome matching conditions are needed for the C-PINN method,compared with the previous studies based on matched asymptotic expansions.

关 键 词：physics-informed neural network(PINN) singular perturbation boundarylayer problem composite asymptotic expansion 

分 类 号：O302[理学—力学]