Solving 2D Poisson's equation based on conditional generative adversarial network

Abstract

AbstractThe numerical simulation of electromagnetic problems is usually complex and time‐consuming, so a fast and accurate solver is urgently needed. In this paper, a deep learning method based on conditional generative adversarial network (CGAN) is used to solve the 2D Poisson's equation in electrostatic field. The relative permittivity distribution and source charge distribution in the two dimensional region are regarded as label of CGAN, and the potential distribution is the real image or generated image corresponding to the label. This deep learning network can be trained by reasonably designing the loss functions of generator and discriminator, and based on a large amount of samples obtained by the finite difference method. The average relative prediction error of the trained CGAN for all samples is less than 0.5%, with a significant reduction in prediction time, while that of convolution neural network (CNN) is less than 1.5%. Furthermore, the average relative prediction error of CGAN is less than 1% for the scenes different from those of training and testing samples, including triangle, square, and pentagon. The prediction results indicate that CGAN has stronger learning ability and fast prediction speed, and can be used as a fast solver for electromagnetic numerical problems.