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We propose a stochastic gradient descent approach with partitioned-truncatedsingular value decomposition for large-scale inverse problems of magneticmodulus data. Motivated by a uniqueness theorem in gravity inverse problem andrealizing the similarity between gravity and magnetic inverse problems, wepropose to solve the level-set function modeling the volume susceptibilitydistribution from the nonlinear magnetic modulus data. To deal with large-scaledata, we employ a mini-batch stochastic gradient descent approach with randomreshuffling when solving the optimization problem of the inverse problem. Wepropose a stepsize rule for the stochastic gradient descent according to theCourant-Friedrichs-Lewy condition of the evolution equation. In addition, wedevelop a partitioned-truncated singular value decomposition algorithm for thelinear part of the inverse problem in the context of stochastic gradientdescent. Numerical examples illustrate the efficacy of the proposed method,which turns out to have the capability of efficiently processing large-scalemeasurement data for the magnetic inverse problem. A possible generalization tothe inverse problem of deep neural network is discussed at the end.

inverse problems

A stochastic gradient descent approach with partitioned-truncated  singular value decomposition for large-scale inverse problems of magnetic  modulus data