Solving Electromagnetic Inverse Problem Using Adaptive Gradient Descent Algorithm

作者：Lian Liu, Bo Yang, Yi Zhang, Yixian Xu, Zhong Peng, Feng Wang · 发表于：IEEE Transactions on Geoscience and Remote Sensing · 年份：2023 · DOI：10.1109/tgrs.2023.3239106 · 被引用次数：12 · 研究领域：Geophysical and Geoelectrical Methods、Geophysical Methods and Applications、Seismic Waves and Analysis

The nonlinear conjugate gradient (NLCG) algorithm is one of the popular linearized methods used to solve the frequency-domain electromagnetic (EM) geophysical inverse problem. During NLCG iterations, the model gradient guides the searching direction while the line-search algorithm determines the step length of each iteration. Normally, the line search requires solving the corresponding forward problem a few times. Since line search is usually computationally inefficient, we introduce the adaptive gradient descent (AGD) algorithm to accelerate solving the frequency-domain EM inverse problem within the linearized framework. The AGD algorithm is a variant of the classical gradient descent method and has been well-developed and widely used in deep learning. Rather than the time-consuming line search, its core idea is to algebraically manipulate the cumulative gradients and updates of the model from previous iterations to estimate the model parameter variables at the current iteration. For the inversion of magnetotelluric (MT) data, we here designed and implemented a framework using the AGD algorithm combined with the cool-down scheme to tune the regularization parameter. To improve the convergence performance of the AGD algorithm [specifying to Adam and root-mean-square propagation (RMSProp)], we proposed a tolerance strategy which has been tested numerically. To optimize the global learning rate, we carried out some comparative trials in the proposed inversion framework. The inv...