A Maxwell's Equations Based Deep Learning Method for Time Domain Electromagnetic Simulations

In this paper, we discuss an unsupervised deep learning (DL) method for solving time domain electromagnetic simulations. Compared to the conventional approach, our method encodes initial conditions, boundary conditions as well as Maxwell's equations as the constraints when training the network, turning an electromagnetic simulation problem into an optimization process. High prediction accuracy of the electromagnetic fields, without discretization or interpolation in space or in time, can be achieved with limited number of layers and neurons in each layer of the neural network. We study several numerical examples to demonstrate the effectiveness of this method for simulating time-domain electromagnetic fields. First, the accuracy of this method is validated by comparing with the analytical solution of a 1D cavity model filled with homogeneous media. Then, we combine the continuity condition to modify the loss function for handling medium discontinuities. Further, the computational efficiency of finite-difference and DL methods in conductive and nonlinear media is compared. Finally, we prove the effectiveness of this method in high-dimensional and multi-scale simulations.