Study on a Poisson's Equation Solver Based On Deep Learning Technique
This work demonstrates a faster alternative to traditional numerical solvers for Poisson's equation, which is relevant for computational physics and engineering applications.
The paper applies a deep convolutional neural network to solve Poisson's equation, achieving prediction errors below 1.5% for 2D and below 3% for 3D cases with significant CPU time reduction compared to finite difference methods.
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.