The Calderón's problem via DeepONets

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.

32 pp.; contribution to the special issue dedicated to Carlos Kenig's 70th birthday. Considered comments and suggestions by the referees