The Equivalence and Realization of Neural Network and Finite Differences Time Domain

Finite Differences-Time Domain (FDTD) is a proven method for numerical calculation and simulation of the electromagnetic field. However, the speed of FDTD slows down dramatically as the size of the simulation space increases. To tackle this problem, two convolutional neural networks, with explainable weights (CNN-A) and unexplainable weights (CNN-B), are proposed in this paper. Numerical examples and comprehensive analysis are provided to benchmark these two networks. The results and analysis demonstrate that CNN-A can reduce the time cost by 20.8% with 100% accuracy compared to the traditional FDTD method. After training with a few samples, CNN-B can reach satisfying accuracy with average 19.8% decrement of time cost comparing with the traditional FDTD method.