Electrostatic Field Simulation Using Deep Learning

Abstract

Some deep learning-based methods have recently been suggested for solving partial differential equations. In these methods, a loss function for training a deep neural network is formulated to satisfy differential operators, boundary conditions, and initial conditions of the intended partial differential equation. After the training, the approximate solution of the partial differential equation can be obtained as a continuous function for the independent variables, specifically a neural network with learned parameters. In this paper, we describe how to solve partial differential equations using deep learning in detail and apply the deep learning-based method to an electrostatic field simulation to solve the Laplace equation. As a result, approximated solutions obtained by the deep learning-based method show generally good agreement with the analytical solutions.