Szczegóły publikacji
Opis bibliograficzny
Comparison of physics informed neural networks and finite element method solvers for advection-dominated diffusion problems / Maciej SIKORA, Patryk Krukowski, Anna PASZYŃSKA, Maciej PASZYŃSKI // Journal of Computational Science ; ISSN 1877-7503. — 2024 — vol. 81 art. no. 102340, s. 1-11. — Bibliogr. s. 11, Abstr. — Publikacja dostępna online od: 2024-06-10. — A. Paszyńska - dod. afiliacja: Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Krakow, Poland
Autorzy (4)
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 153749 |
|---|---|
| Data dodania do BaDAP | 2024-06-19 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.jocs.2024.102340 |
| Rok publikacji | 2024 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Journal of Computational Science |
Abstract
We present a comparison of Physics Informed Neural Networks (PINN) and Variational Physics Informed Neural Networks (VPINN) with higher-order and continuity Finite Element Method (FEM). We focus on the one-dimensional advection-dominated diffusion problem and the two-dimensional Eriksson–Johnson model problem. We show that the standard Galerkin method for FEM cannot solve this problem on uniform grid. We discuss the stabilization of the advection-dominated diffusion problem with the Petrov–Galerkin (PG) formulation and present the FEM solution obtained with the PG method. The main benefit of using a stabilization method is that it can deliver a good-quality approximation to the solution on a mesh that is not fully refined towards the singularity. We employ PINN and VPINN methods, defining several strong and weak loss functions. We compare the training and solutions of PINN and VPINN methods with higher-order FEM methods. We consider a case with uniform FEM and uniform distribution of points for PINN, as well as uniform distribution of test functions for VPINN. We also consider adaptive FEM, refined towards edge singularity, and non-uniform distribution of points for PINN, as well as non-uniform distribution of test functions for VPINN.
