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Maxim Shishlenin | Electroacoustic tomography: inverse problems and deep learning
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Days on Diffraction 2024. Mini-symposium “Inverse Problems”. Tuesday, 11 June, 2024
Maxim A. Shishlenin (Sobolev Institute of Mathematics, Institute of Computational Mathematics and Mathematical Geophysics),
Nikita S. Novikov (Sobolev Institute of Mathematics, Institute of Computational Mathematics and Mathematical Geophysics),
Sergey I. Kabanikhin (Sobolev Institute of Mathematics, Institute of Computational Mathematics and Mathematical Geophysics)
Electroacoustic tomography: inverse problems and deep learning
The inverse problems of electro acoustic tomography [1] are considered, the mathematical model of which is based on conservation laws. A combined formulation of the inverse problem for a system of equations of acoustics and electrodynamics for determining acoustic and electromagnetic parameters of the medium from measurements at the boundary of the studied region is investigated [2]. A mathematical model has been developed that allows monitoring compliance with conservation laws and allows parallelization in solving direct and inverse problems on a supercomputer.
The inverse problem is reduced to minimizing the target functional by the gradient descent method [3]. The results of numerical calculations using machine learning technology are presented. A comparative analysis of model-driven and data-driven methods is carried out. The work was performed within the framework of the state assignment of the S. L. Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project FWNF- 2024-0001.
Maxim A. Shishlenin (Sobolev Institute of Mathematics, Institute of Computational Mathematics and Mathematical Geophysics),
Nikita S. Novikov (Sobolev Institute of Mathematics, Institute of Computational Mathematics and Mathematical Geophysics),
Sergey I. Kabanikhin (Sobolev Institute of Mathematics, Institute of Computational Mathematics and Mathematical Geophysics)
Electroacoustic tomography: inverse problems and deep learning
The inverse problems of electro acoustic tomography [1] are considered, the mathematical model of which is based on conservation laws. A combined formulation of the inverse problem for a system of equations of acoustics and electrodynamics for determining acoustic and electromagnetic parameters of the medium from measurements at the boundary of the studied region is investigated [2]. A mathematical model has been developed that allows monitoring compliance with conservation laws and allows parallelization in solving direct and inverse problems on a supercomputer.
The inverse problem is reduced to minimizing the target functional by the gradient descent method [3]. The results of numerical calculations using machine learning technology are presented. A comparative analysis of model-driven and data-driven methods is carried out. The work was performed within the framework of the state assignment of the S. L. Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project FWNF- 2024-0001.