论文标题
一种随机梯度下降方法，具有分区截断的奇异值分解，用于大规模磁模量数据的大规模逆问题
A stochastic gradient descent approach with partitioned-truncated singular value decomposition for large-scale inverse problems of magnetic modulus data
论文作者
论文摘要
我们提出了一种随机梯度下降方法，用于用于磁模量数据的大规模逆问题的分区截断的奇异值分解。由重力逆问题的唯一定理和实现重力和磁反问题之间的相似性的动机，我们建议求解从非线性磁模量数据中建模体积易感性分布的水平函数。为了处理大规模数据，我们在解决反问题的优化问题时采用了一个迷你批量随机梯度下降方法，并随机重新安装。我们根据进化方程的Courant-Friedrichs-Lewy条件为随机梯度下降提出了一个步骤规则。此外，在随机梯度下降的背景下，我们为反问题的线性部分开发了分区截断的奇异值分解算法。数值示例说明了所提出的方法的功效，事实证明，该方法具有有效处理磁反问题的大规模测量数据的能力。最后讨论了对深神经网络的反问题的可能概括。
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.
