Study on a Fast Solver for Poisson's Equation Based on Deep Learning Technique

Fast and efficient computational electromagnetic simulation is a long-standing challenge. In this article, we propose a data-driven model to solve Poisson's equation that leverages the learning capacity of deep learning techniques. A deep convolutional neural network (ConvNet) is trained to predict the electric potential with different excitations and permittivity distribution in 2-D and 3-D models. With a careful design of cost function and proper training data generated from finite-difference solvers, the proposed network enables a reliable simulation with significant speedup and fairly good accuracy. Numerical experiments show that the same ConvNet architecture is effective for both 2-D and 3-D models, and the average relative prediction error of the proposed ConvNet model is less than 3% in both 2-D and 3-D simulations with a significant reduction in computation time compared to the finite-difference solver. This article shows that deep neural networks have a good learning capacity for numerical simulations. This could help us to build some fast solvers for some computational electromagnetic problems.