Two-dimensional Klein-Gordon and Sine-Gordon numerical solutions based on deep neural network

Abstract

Due to the well-known dimensionality curse, developing effective numerical techniques to resolve partial differential equations proved a complex problem. We propose a deep learning technique for solving these problems. Feedforward neural networks (FNNs) use to approximate a partial differential equation with more robust and weaker boundaries and initial conditions. The framework called PyDEns could handle calculation fields that are not regular. Numerical exper- iments on two-dimensional Sine-Gordon and Klein-Gordon systems show the provided frameworks to be sufficiently accurate.