Deep neural network solutions to Newell-Whitehead-Segel equations

Abstract

In this work, we use the deep neural network (DNN) approach called NeuroDiffEq, and the unified finite difference exponential approach for obtaining the approximated and exact solutions of Newell-Whitehead-Segel systems that are essential for the biology of mathematics. A unified approach was used to generate several solutions for solitary waves of those systems. The approximated solutions for selected studies are explored using the NeuroDiffEq approach, which is the artificial neural networks (ANN) approach and is based upon trial approximate solution (TAS). The comparison between the obtained approximated solutions and the analytical solutions indicates that the applied method has proved an efficient as well as a highly successful approach to solving various types of the Newell-Whitehead-Segel equations.