Szczegóły publikacji
Opis bibliograficzny
Robust variational physics-informed neural networks / Sergio Rojas, Paweł MACZUGA, Judit Muñoz-Matute, David Pardo, Maciej PASZYŃSKI // Computer Methods in Applied Mechanics and Engineering ; ISSN 0045-7825. — 2024 — vol. 425 art. no. 116904, s. 1-18. — Bibliogr. s. 17-18, Abstr. — Publikacja dostępna online od: 2024-03-18
Autorzy (5)
- Rojas Sergio
- AGHMaczuga Paweł
- Muñoz-Matute Judit
- Pardo David
- AGHPaszyński Maciej
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 152514 |
|---|---|
| Data dodania do BaDAP | 2024-04-19 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.cma.2024.116904 |
| Rok publikacji | 2024 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Computer Methods in Applied Mechanics and Engineering |
Abstract
We introduce a Robust version of the Variational Physics-Informed Neural Networks method (RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a Petrov–Galerkin-type variational formulation of the PDE problem: the trial space is a (Deep) Neural Network (DNN) manifold, while the test space is a finite-dimensional vector space. Whereas the VPINN’s loss depends upon the selected basis functions of a given test space, herein, we minimize a loss based on the discrete dual norm of the residual. The main advantage of such a loss definition is that it provides a reliable and efficient estimator of the true error in the energy norm under the assumption of the existence of a local Fortin operator. We test the performance and robustness of our algorithm in several advection–diffusion problems. These numerical results perfectly align with our theoretical findings, showing that our estimates are sharp.