Applied Mathematics and Mechanics >
Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems
Received date: 2024-07-31
Online published: 2024-08-27
Supported by
the National Natural Science Foundation of China Basic Science Center Program for “Multiscale Problems in Nonlinear Mechanics”(11988102);the National Natural Science Foundation of China(12202451);Project supported by the National Natural Science Foundation of China Basic Science Center Program for “Multiscale Problems in Nonlinear Mechanics” (No. 11988102) and the National Natural Science Foundation of China (No. 12202451)
Copyright
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 well-known 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.
Long WANG, Lei ZHANG, Guowei HE . Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems[J]. Applied Mathematics and Mechanics, 2024 , 45(9) : 1467 -1480 . DOI: 10.1007/s10483-024-3149-8
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