Two-level deep domain decomposition method
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916365909098496 |
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| author | Dolean, Victorita Gratton, Serge Heinlein, Alexander Mercier, Valentin |
| author_facet | Dolean, Victorita Gratton, Serge Heinlein, Alexander Mercier, Valentin |
| contents | This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs). The addition of the coarse level network improves scalability and convergence rates compared to the single level method. Tested on a Poisson equation with Dirichlet boundary conditions, the two-level deep DDM demonstrates superior performance, maintaining efficient convergence regardless of the number of subdomains. This advance provides a more scalable and effective approach to solving complex partial differential equations with machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-level deep domain decomposition method Dolean, Victorita Gratton, Serge Heinlein, Alexander Mercier, Valentin Machine Learning Artificial Intelligence This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs). The addition of the coarse level network improves scalability and convergence rates compared to the single level method. Tested on a Poisson equation with Dirichlet boundary conditions, the two-level deep DDM demonstrates superior performance, maintaining efficient convergence regardless of the number of subdomains. This advance provides a more scalable and effective approach to solving complex partial differential equations with machine learning. |
| title | Two-level deep domain decomposition method |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2408.12198 |