The Calderón's problem via DeepONets
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866929312748273664 |
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| author | Castro, Javier Muñoz, Claudio Valenzuela, Nicolás |
| author_facet | Castro, Javier Muñoz, Claudio Valenzuela, Nicolás |
| contents | We consider the Dirichlet-to-Neumann operator and the direct and inverse Calderón's mappings appearing in the Inverse Problem of recovering a smooth bounded and positive isotropic conductivity of a material filling a smooth bounded domain in space. Using deep learning techniques, we prove that these mappings are rigorously approximated by DeepONets, infinite-dimensional counterparts of standard artificial neural networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08941 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Calderón's problem via DeepONets Castro, Javier Muñoz, Claudio Valenzuela, Nicolás Analysis of PDEs Numerical Analysis We consider the Dirichlet-to-Neumann operator and the direct and inverse Calderón's mappings appearing in the Inverse Problem of recovering a smooth bounded and positive isotropic conductivity of a material filling a smooth bounded domain in space. Using deep learning techniques, we prove that these mappings are rigorously approximated by DeepONets, infinite-dimensional counterparts of standard artificial neural networks. |
| title | The Calderón's problem via DeepONets |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2212.08941 |