On the Solution of Poisson’s Equation using Deep Learning

We devise a numerical method for solving the Poisson’s equation using a convolutional neural network architecture, otherwise known as deep learning. The method we have employed here uses both feedforward neural systems and backpropagation to set up a framework for achieving the numerical solutions of the elliptic partial differential equations - more superficially the Poisson’s equation. Our deep learning framework has two substantial entities. The first part of the network enables to fulfill the necessary boundary conditions of the Poisson’s equation while the second part consisting of a feedforward neural system containing flexible parameters or weights gives rise to the solution. We have compared the solutions of the Poisson’s equation arising from our deep learning framework subject to various boundary conditions with the corresponding analytic solutions. As a result, we have found that our deep learning framework can obtain solutions which are accurate as well as efficient.