The Calder\'on's problem via DeepONets
Analysis of PDEs
2024-04-16 v3 Numerical Analysis
Numerical Analysis
Abstract
We consider the Dirichlet-to-Neumann operator and the direct and inverse Calder\'on'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.
Cite
@article{arxiv.2212.08941,
title = {The Calder\'on's problem via DeepONets},
author = {Javier Castro and Claudio Muñoz and Nicolás Valenzuela},
journal= {arXiv preprint arXiv:2212.08941},
year = {2024}
}
Comments
32 pp.; contribution to the special issue dedicated to Carlos Kenig's 70th birthday. Considered comments and suggestions by the referees