The Calderón's problem via DeepONets

2022/12/17 by Javier Castro, Claudio Muñoz, Castro, Javier +3 · 1 citation
Earth and Planetary Sciences · Mathematics · Computer Science · #Geophysical and Geoelectrical Methods #Numerical methods in inverse problems #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2212.08941

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.

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