Szczegóły publikacji
Opis bibliograficzny
An h-adaptive collocation method for Physics-Informed Neural Networks / Jan Trynda, Paweł MACZUGA, Albert Oliver-Serra, Luis Emilio García-Castillo, Robert SCHAEFER, Maciej WOŹNIAK // Journal of Computational Science ; ISSN 1877-7503. — 2025 — vol. 91 art. no. 102684, s. 1–14. — Bibliogr. s. 13–14, Abstr. — Publikacja dostępna online od: 2025-07-25
Autorzy (6)
- AGHTrynda Jan
- AGHMaczuga Paweł
- Oliver-Serra Albert
- Garcia-Castillo Luis E.
- AGHSchaefer Robert
- AGHWoźniak Maciej
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 161713 |
|---|---|
| Data dodania do BaDAP | 2025-08-28 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.jocs.2025.102684 |
| Rok publikacji | 2025 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Journal of Computational Science |
Abstract
Despite their flexibility and success in solving partial differential equations, Physics-Informed Neural Networks (PINNs) often suffer from convergence issues, even failing to converge, particularly in problems with steep gradients or localized features. Several remedies have been suggested to solve this problem, but one of the most promising is the dynamical adaptation of the collocation points. This paper explores a novel adaptive sampling method, of a stochastic nature, based on the Adaptive Mesh Refinement used in the Finite Element Method. The error estimates in our refinement algorithm are based on the value of the residual loss function. We tested our method against a variety of 1D and 2D benchmark problems that exhibit steep gradients near certain boundaries, with promising results.
