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Application of neural networks in nonlinear inverse problems of geophysics. (English. Russian original) Zbl 1450.86004
Comput. Math. Math. Phys. 60, No. 6, 1025-1036 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 6, 1053-1065 (2020).
Summary: Neural networks (NN) are widely used for solving various problems of geophysical data interpretation and processing. The application of the neural network approximation (NNA) method for solving inverse problems, including inverse multicriteria problems of geophysics that are reduced to a nonlinear operator equation of first kind (respectively, to a system of operator equations) is considered. The NNA method assumes the construction of an approximate inverse operator of the problem using neural network approximation designs (MLP networks) on the basis of a preliminary constructed set of reference solutions to direct and inverse problems. A review of the application of the NNA method for solving nonlinear inverse problems of geophysics is given. Techniques for estimating the practical ambiguity (error) of approximate solutions to inverse multicriteria problems are considered. Results of solving the inverse two-criteria 2D gravimetry problem in combination with magnetometry are presented.
MSC:
86A22 Inverse problems in geophysics
86-08 Computational methods for problems pertaining to geophysics
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