Szczegóły publikacji
Opis bibliograficzny
Three-dimensional collocation-based robust variational physics informed neural networks / Tomasz SŁUŻALEC, Marcin ŁOŚ, Maciej PASZYŃSKI // W: Computational Science – ICCS 2026 : 26th International Conference : Hamburg, Germany, June 29–July 1, 2026 : proceedings , Pt. 2 / eds. Philipp Neumann [et al.]. — Cham : Springer, cop. 2026. — ( Lecture Notes in Computer Science ; ISSN 0302-9743 ; LNCS 16784 ). — ISBN: 978-3-032-29923-9; e-ISBN: 978-3-032-29924-6. — S. 567–574. — Bibliogr., Abstr. — Publikacja dostępna online od: 2026-06-27
Autorzy (3)
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 168889 |
|---|---|
| Data dodania do BaDAP | 2026-08-28 |
| DOI | 10.1007/978-3-032-29924-6_53 |
| Rok publikacji | 2026 |
| Typ publikacji | materiały konferencyjne (aut.) |
| Otwarty dostęp |  |
| Wydawca | Springer |
| Konferencja | International Conference on Computational Science 2026 |
| Czasopismo/seria | Lecture Notes in Computer Science |
Abstract
Physics Informed Neural Networks (PINNs) are an increasingly popular approach to utilizing tools and infrastructure developed for neural network training to solve PDEs. While the mainstream approach is based on strong formulations, Variational PINNs (VPINNs) have been proposed to tackle problems with lower regularity. Their issues with robustness, which manifest as a disconnect between the value of the loss function used for training and the error in the relevant Sobolev norm , can be alleviated by employing Robust Variational PINNs (RVPINNs) at the expense of efficiency due to the cost of integrating terms involving the neural network and factorizing the Gram matrix. Collocation-based Robust Variational PINNs (CRVPINN) aim to regain the efficiency of PINNs while retaining robustness by applying the RVPINN framework to variational formulations based on discrete grids and finite difference approximations.Here, we extend the CRVPINN method to 3D and validate it on Poisson and advection-diffusion problems.
