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.

翻译：我们考虑Dirichlet-to-Neumann算子以及出现在逆问题中的正向和逆Calderón映射，该逆问题旨在恢复空间中光滑有界域内填充材料的平滑、有界且正各向同性导电率。利用深度学习技术，我们证明这些映射可以被DeepONet——标准人工神经网络的无限维对应物——严格逼近。