Szczegóły publikacji
Opis bibliograficzny
Accelerating training of Physics Informed Neural Network for 1D PDEs with hierarchical matrices / Mateusz Dobija, Anna PASZYŃSKA, Carlos Uriarte, Maciej PASZYŃSKI // W: Computational Science – ICCS 2024 : 24th International Conference : Malaga, Spain, July 2–4, 2024 : proceedings, Pt. 3 / eds. Leonardo Franco, [et al.]. — Cham : Springer, cop. 2024. — (Lecture Notes in Computer Science ; ISSN 0302-9743 ; 14834). — ISBN: 978-3-031-63758-2; e-ISBN: 978-3-031-63759-9. — S. 352–362. — Bibliogr., Abstr. — Publikacja dostępna online od: 2024-06-29. — A. Paszyńska - dod. afiliacja: Jagiellonian University, Krakow
Autorzy (4)
- Dobija Mateusz
- AGHPaszyńska Anna
- Uriarte Carlos
- AGHPaszyński Maciej
Dane bibliometryczne
| ID BaDAP | 154321 |
|---|---|
| Data dodania do BaDAP | 2024-07-11 |
| DOI | 10.1007/978-3-031-63759-9_38 |
| Rok publikacji | 2024 |
| Typ publikacji | materiały konferencyjne (aut.) |
| Otwarty dostęp |  |
| Wydawca | Springer |
| Konferencja | International Conference on Computational Science 2024 |
| Czasopismo/seria | Lecture Notes in Computer Science |
Abstract
In this paper, we consider a training of Physics Informed Neural Networks with fully connected neural networks for approximation of solutions of one-dimensional advection-diffusion problem. In this context, the neural network is interpreted as a non-linear function of one spatial variable, approximating the solution scalar field, namely y = PINN(x) = Anσ(An-1...A2σ(A1 + b1) + b2) + ... + bn-1) + bn. In the standard PINN approach, the Ai denotes dense matrices, bi denotes bias vectors, and σ is the non-linear activation function (sigmoid in our case). In our paper, we consider a case when Ai are hierarchical matrices Ai = Hi. We assume a structure of our hierarchical matrices approximating the structure of finite difference matrices employed to solve analogous PDEs. In this sense, we propose a hierarchical neural network for training and approximation of PDEs using the PINN method. We verify our method on the example of a one-dimensional advection-diffusion problem.
