Artificial neural network-enhanced unconditionally stable finite-difference time-domain technique for multiscale problems

Electromagnetic sensing and system-level design challenges are often multiscale in nature, making them difficult to solve. These challenges will likely continue to hinder system-level sensing and design optimization for the foreseeable future. Typically, such multiscale problems involve three electrical scales: the fine scale, the coarse scale, and the intermediate scale that lies between them. The significant differences in scale across both spatial and temporal domains present major difficulties in numerical modeling and simulation. In this paper, a new artificial neural network (ANN) and unconditionally stable finite-difference time-domain (FDTD) technique for multiscale problems is proposed. The field data at these points is the output of ANN-FDTD, which takes as its input the point position of the spatial grid division in FDTD. Every time step, the output of the ANN and a known forced excitation source were used to build the hypothetical solution of Maxwell's equations. The gradient of the ANN's output with respect to the input vector indicates the error of the system. Labeled samples are not required for training as the backpropagation (BP) algorithm uses this error value to update the ANN parameters. In this case, ANN is trained to guarantee that the boundary requirements are satisfied by the hypothetical response. Every time-marching phase involves training a different ANN, so the results from one step do not impact the results from the next. With finely structured microwave components, the time step of the ANN-FDTD can be selected to be substantially bigger than that of the conventional FDTD. In addition, it is possible to partition each time step into blocks for parallel calculation. The accuracy and effectiveness of the proposed technique are verified by three numerical examples. The proposed method finds applications in antenna design, metamaterials, wireless communications, and wave propagation in complex environments.