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

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...

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Veröffentlicht in:Applied mathematics and mechanics Jg. 45; H. 9; S. 1467 - 1480
Hauptverfasser: Wang, Long, Zhang, Lei, He, Guowei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024
Springer Nature B.V
The State Key Laboratory of Nonlinear Mechanics,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China
School of Engineering Sciences,University of Chinese Academy of Sciences,Beijing 100049,China
Ausgabe:English ed.
Schlagworte:
Applications of Mathematics
Applied mathematics
Approximation
Asymptotic methods
Asymptotic series
Boundary conditions
Classical Mechanics
Differential equations
Fluid mechanics
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Neural networks
Ordinary differential equations
Partial Differential Equations
Physics
Science
Singular perturbation
Thin plates
68T01
O302
singular perturbation
physics-informed neural network (PINN)
composite asymptotic expansion
boundary-layer problem
34E15
physics-informed neural network(PINN)
ISSN:0253-4827, 1573-2754, 1573-2754
Online-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0253-4827
1573-2754
1573-2754
DOI:10.1007/s10483-024-3149-8