Open AccessThe approximation neural-network method for solving nonlinear multi-criteria inverse problems of geophysics
Author(s) -
Mikhail Shimelevich,
Eugeny Obornev,
Ivan Obornev,
Eugeny Rodionov
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1715/1/012045
Subject(s) - inverse problem , a priori and a posteriori , artificial neural network , nonlinear system , inverse , mathematics , operator (biology) , mathematical optimization , approximation error , computer science , mathematical analysis , artificial intelligence , physics , geometry , philosophy , biochemistry , chemistry , epistemology , repressor , quantum mechanics , transcription factor , gene
A multi-criteria inverse problem is reduced to a system of operator equations on compact sets. It is shown that some a posteriori error estimates of solutions of the multi-criteria problem decrease with an increasing number of the criteria used. The approximation neural-network method for solving the multi-criteria inverse problem is presented. An example of a numerical solution of the two-criterion problem of geoelectrics is given, and the a posteriori error estimates are calculated.