Geodesic
An algorithm for solving an inverse geoelectrics problem based on the neural network approximation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 4, pp. 451-468

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The approximation neural network algorithm for solving the inverse geoelectrics problems in the class of grid (block) media models is presented. The algorithm is based on constructing an approximate inverse operator using neural networks and makes it possible to formally obtain solutions of the inverse geoelectrics problem with the total number of desired parameters of the medium $\sim n\cdot103$. The correctness of the problem of constructing the neural network inverse operators is considered. A posteriori estimates of the degree of ambiguity of the inverse problem solutions are calculated. The operation of the algorithm is illustrated by examples of the 2D, the 3D inversions of synthesized and field geoelectric data, obtained by the MTS method. 
@article{SJVM_2018_21_4_a7,
     author = {M. I. Shimelevich and E. A. Obornev and I. E. Obornev and E. A. Rodionov},
     title = {An algorithm for solving an inverse geoelectrics problem based on the neural network approximation},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {451--468},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2018_21_4_a7/}
}
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M. I. Shimelevich; E. A. Obornev; I. E. Obornev; E. A. Rodionov. An algorithm for solving an inverse geoelectrics problem based on the neural network approximation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 4, pp. 451-468. http://geodesic.mathdoc.fr/item/SJVM_2018_21_4_a7/