Title: Study on a Poisson's Equation Solver Based On Deep Learning Technique,
Abstract: In this work, we investigated the feasibility of applying deep learning
techniques to solve Poisson's equation. A deep convolutional neural network is
set up to predict the distribution of electric potential in 2D or 3D cases.
With proper training data generated from a finite difference solver, the strong
approximation capability of the deep convolutional neural network allows it to
make correct prediction given information of the source and distribution of
permittivity. With applications of L2 regularization, numerical experiments
show that the predication error of 2D cases can reach below 1.5\% and the
predication of 3D cases can reach below 3\%, with a significant reduction in
CPU time compared with the traditional solver based on finite difference
methods.