The Calderón's Problem via DeepONets

Castro J.; Munoz, C; Valenzuela N.

Keywords: approximation, numerical analysis, inverse problems, deep learning, Calderon's problem, Operator learning

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.

Más información

Título según WOS: The Calderón's Problem via DeepONets
Título según SCOPUS: The Calderón’s Problem via DeepONets
Título de la Revista: Vietnam Journal of Mathematics
Volumen: 52
Número: 3
Editorial: Springer
Fecha de publicación: 2024
Página de inicio: 775
Página final: 806
Idioma: English
DOI:

10.1007/s10013-023-00674-8

Notas: ISI, SCOPUS