  We propose a stochastic gradient descent approach with partitioned-truncated
singular value decomposition for large-scale inverse problems of magnetic
modulus data. Motivated by a uniqueness theorem in gravity inverse problem and
realizing the similarity between gravity and magnetic inverse problems, we
propose to solve the level-set function modeling the volume susceptibility
distribution from the nonlinear magnetic modulus data. To deal with large-scale
data, we employ a mini-batch stochastic gradient descent approach with random
reshuffling when solving the optimization problem of the inverse problem. We
propose a stepsize rule for the stochastic gradient descent according to the
Courant-Friedrichs-Lewy condition of the evolution equation. In addition, we
develop a partitioned-truncated singular value decomposition algorithm for the
linear part of the inverse problem in the context of stochastic gradient
descent. Numerical examples illustrate the efficacy of the proposed method,
which turns out to have the capability of efficiently processing large-scale
measurement data for the magnetic inverse problem. A possible generalization to
the inverse problem of deep neural network is discussed at the end.
