Solving Time Domain Electromagnetic Problems using a Differentiable Programming Platform

Abstract

Deep-learning techniques have been playing an increasingly important role for scientific modeling and simulations. Recent advances in high-performance tensor processing hardware and software are also providing new opportunities for accelerated linear algebra calculations. In this paper, we exploit a trainable recurrent neural network (RNN) to formulate the electromagnetic propagation and solve the Maxwell's equations on one of the most state-of-the-art differentiable programming platforms—Pytorch. Due to the specific performance-focused design of PyTorch, the computation efficiency is substantially improved compared to Matlab. Moreover, RNN-based implementation possesses potential advantages of leveraging the differentiable programming platform for varied applications that iterate around forward modeling, for example, uncertainty quantification, optimization, and inversion. Numerical simulation demonstrates the effectiveness of our method.