The Calderón's Problem via DeepONets
Castro Medina J, Munoz C, Valenzuela N (2024)
Vietnam Journal of Mathematics .
Zeitschriftenaufsatz
| E-Veröff. vor dem Druck | Englisch
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Autor*in
Castro Medina, JavierUniBi;
Munoz, Claudio;
Valenzuela, Nicolas
Abstract / Bemerkung
We consider the Dirichlet-to-Neumann operator and the direct and inverse Calderon'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.
Stichworte
Inverse problems;
Calderon's problem;
Deep learning;
Operator learning;
Approximation;
Numerical analysis
Erscheinungsjahr
2024
Zeitschriftentitel
Vietnam Journal of Mathematics
ISSN
2305-221X
eISSN
2305-2228
Page URI
https://pub.uni-bielefeld.de/record/2986267
Zitieren
Castro Medina J, Munoz C, Valenzuela N. The Calderón's Problem via DeepONets. Vietnam Journal of Mathematics . 2024.
Castro Medina, J., Munoz, C., & Valenzuela, N. (2024). The Calderón's Problem via DeepONets. Vietnam Journal of Mathematics . https://doi.org/10.1007/s10013-023-00674-8
Castro Medina, Javier, Munoz, Claudio, and Valenzuela, Nicolas. 2024. “The Calderón's Problem via DeepONets”. Vietnam Journal of Mathematics .
Castro Medina, J., Munoz, C., and Valenzuela, N. (2024). The Calderón's Problem via DeepONets. Vietnam Journal of Mathematics .
Castro Medina, J., Munoz, C., & Valenzuela, N., 2024. The Calderón's Problem via DeepONets. Vietnam Journal of Mathematics .
J. Castro Medina, C. Munoz, and N. Valenzuela, “The Calderón's Problem via DeepONets”, Vietnam Journal of Mathematics , 2024.
Castro Medina, J., Munoz, C., Valenzuela, N.: The Calderón's Problem via DeepONets. Vietnam Journal of Mathematics . (2024).
Castro Medina, Javier, Munoz, Claudio, and Valenzuela, Nicolas. “The Calderón's Problem via DeepONets”. Vietnam Journal of Mathematics (2024).
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