| Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems | |
Wang L(王笼)1,2; Zhang L(张磊)1,2; He GW(何国威)1,2
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| Corresponding Author | Zhang, Lei([email protected]) |
| Source Publication | APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
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| 2024-09-01 | |
| Volume | 45Issue:9Pages:1467-1480 |
| ISSN | 0253-4827 |
| Abstract | 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. |
| Keyword | physics-informed neural network (PINN) singular perturbation boundary-layer problem composite asymptotic expansion O302 |
| DOI | 10.1007/s10483-024-3149-8 |
| Indexed By | SCI ; EI ; CSCD |
| Language | 英语 |
| WOS ID | WOS:001303646900009 |
| WOS Keyword | HIGHER APPROXIMATIONS |
| WOS Research Area | Mathematics ; Mechanics |
| WOS Subject | Mathematics, Applied ; Mechanics |
| Funding Project | National Natural Science Foundation of China Basic Science Center Program for Multiscale Problems in Nonlinear Mechanics[11988102] ; National Natural Science Foundation of China[12202451] |
| Funding Organization | National Natural Science Foundation of China Basic Science Center Program for Multiscale Problems in Nonlinear Mechanics ; National Natural Science Foundation of China |
| Classification | 一类 |
| Ranking | 1 |
| Contributor | Zhang, Lei |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/96494 |
| Collection | 非线性力学国家重点实验室 |
| Affiliation | 1.Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China; 2.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Wang L,Zhang L,He GW. Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems[J]. APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION,2024,45,9,:1467-1480.Rp_Au:Zhang, Lei |
| APA | 王笼,张磊,&何国威.(2024).Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems.APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION,45(9),1467-1480. |
| MLA | 王笼,et al."Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems".APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION 45.9(2024):1467-1480. |
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