A New Unconditionally Stable FDTD Method Based on Artificial Neural Network

This article presents a new unconditionally stable finite-difference time-domain (FDTD) method combined with the artificial neural network (ANN) for multiscale problems. The input of ANN-FDTD is the point location of spatial grid division in FDTD, and the output is the field data at these points. At each time step, the hypothetical solution of Maxwell’s equations is constructed using a known forced excitation source and the output of ANN. The error of ANN is determined by the gradient of its output with respect to the input vector. This error value is used to update ANN parameters with the backpropagation (BP) algorithm, so the training does not have to involve labeled samples. Here, ANN is trained to ensure that the hypothetical solution satisfies the boundary conditions. ANN is trained individually at each time-marching step, and thus, the results of the previous step do not affect those of the next step. The time step of ANN-FDTD can be chosen much larger than that of the traditional FDTD for microwave components with fine structures. Moreover, all time steps can be divided into blocks to execute parallel computation. Three numerical examples are provided to validate the accuracy and efficiency of the proposed method.