Year: 2025
Type: article
Abstract: . We consider the inverse problem consisting of the reconstruction of an inclusion [Formula: see text] contained in a bounded domain [Formula: see text] from a single pair of Cauchy data [Formula: see text], where [Formula: see text] in [Formula: see text] and [Formula: see text] on [Formula: see text]. We show that the reconstruction algorithm based on the range test, a domain sampling method, can be written as a neural network with a specific architecture. We propose to learn the weights of this network in the framework of supervised learning, and to combine it with a pretrained classifier, with the purpose of distinguishing the inclusions based on their distance from the boundary. The numerical simulations show that this learned range test method provides accurate and stable reconstructions of polygonal inclusions. Furthermore, the results are superior to those obtained with the standard range test method (without learning) and with an end-to-end fully connected deep neural network, a purely data-driven method.
DOI: 10.1137/24m170716x
Authors: Shiwei Sun, Giovanni S. Alberti
Institutions: Southeast University, University of Genoa
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4413294148