Solving partial differential equations by a supervised learning technique, applied for the reaction–diffusion equation

Abstract

Deep learning is a crucial point of valuable intelligence resources to deal with complicated mathematical problems. The effectiveness of deep learning in solving differential equations has been considered over the past few years. Supervision of the learning process requires significant information to be marked in order to train the network. Nevertheless, this approach could not be a helpful strategy in case of unknown differential equations that we have no identified data. In order to address this problem, a new method for solving differential equations will be introduced in this paper using only the boundary and initial conditions. As an efficient method, inadequate monitoring can provide an ideal bed to fix boundary and initial value issues. For verification of the proposed method, a reaction-diffusion equation was performed. This equation has a variety of applications in engineering and science.