Szczegóły publikacji
Opis bibliograficzny
Deep Neural Networks and smooth approximation of PDEs / Kamil Doległo, Maciej PASZYŃSKI, Leszek Demkowicz // W: Computational Science – ICCS 2022 : 22nd international conference : London, UK, June 21–23, 2022 : proceedings, Pt. 2 / eds. Derek Groen, [et al.]. — Cham : Springer Nature Switzerland, cop. 2022. — (Lecture Notes in Computer Science ; ISSN 0302-9743 ; LNCS 13351). — ISBN: 978-3-031-08753-0; e-ISBN: 978-3-031-08754-7. — S. 328–332. — Bibliogr., Abstr. — Publikacja dostępna online od: 2022-06-15
Autorzy (3)
- AGHDoległo Kamil
- AGHPaszyński Maciej
- Demkowicz Leszek
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 140683 |
|---|---|
| Data dodania do BaDAP | 2022-06-24 |
| DOI | 10.1007/978-3-031-08754-7_41 |
| Rok publikacji | 2022 |
| Typ publikacji | materiały konferencyjne (aut.) |
| Otwarty dostęp |  |
| Wydawca | Springer |
| Konferencja | 22nd International Conference on Computational Science |
| Czasopismo/seria | Lecture Notes in Computer Science |
Abstract
We focus on Isogeometric Analysis (IGA) approximations of Partial Differential Equations (PDEs) solutions. We consider linear combinations of high-order and continuity base functions utilized by IGA. Instead of using the Deep Neural Network (DNN), which is the concatenation of linear operators and activation functions, to approximate the solutions of PDEs, we employ the linear combination of higher-order and continuity base functions, as employed by IGA. In this paper, we compare two methods. The first method trains different DNN for each coefficient of the linear computations. The second method trains one DNN for all coefficients of the linear combination. We show on model L-shape domain problem that training several small DNNs learning how to span B-splines coefficients is more efficient.