论文标题
Calderón通过deponets的问题
The Calderón's problem via DeepONets
论文作者
论文摘要
我们考虑到Dirichlet到Neumann运算符，以及直接和逆Calderón的映射，出现在恢复平滑界限和正态的各向同性电导率的倒数问题中，该材料填充了空间中平稳的界面域。使用深度学习技术，我们证明了这些映射是由Deeponets，无限维度对应物的标准人工神经网络严格近似的。
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.
