The Calderón’s problem via DeepONets
- Authors: Javier Castro, Claudio Muñoz, Nicolás Valenzuela
- Preprint year: 2022
- First public date: 2022-12-17
- arXiv: 2212.08941
- Status: Published
- Publication type: Journal article
- Publication year: 2024
- Journal: Vietnam Journal of Mathematics 52, 775–806 (2024)
- DOI: 10.1007/s10013-023-00674-8
Abstract
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.