Rapid surrogate modeling of magnetotelluric in the frequency domain using physics-driven deep neural networks

The magnetotelluric (MT) forward modeling problem primarily relies on spatially discretization of Maxwell's equations using polynomials into an algebraic system with finite dimensions. It is computationally prohibitive to solve the algebraic system, resulting in a slow computational speed. The inversion scheme requires a significant number of forward computations, and the efficiency of the inversion is determined by the forward modeling speed. Therefore, constructing an economical surrogate model as a fast solver for the forward problem can considerably improve the efficiency of inversion. Because of their capacity to approximate, deep neural networks (DNNs) have showed significant potential for surrogating. We present a physics-driven model (PDM) to solve the MT governing equation without using any labeled data. Specifically, the product of conductivity and frequency is used as the input to the DNNs, and the loss function is given by the governing equation to "drive" the training. The trained model is capable in predicting electromagnetic fields at any frequency within the range of trained datasets, even ones that are not presented in the training. Numerical experiments are conducted on 2-D conductivity structures with uniform and non-uniform discretization. The results show excellent agreement on the MT responses between the PDM predictions and the finite-difference method (FDM). In addition, the computing speed of PDM exceeds by multiple times that of FDM.