Orthonormal Bernoulli wavelets neural network method and its application in astrophysics

Abstract

The purpose of this paper is to present two efficient computational schemes for solving Lane–Emden type equations based on an artificial neural network. The mentioned neural network consists of three layers (input layer, hidden layer, output layer). We use orthonormal Bernoulli wavelets and arctanh(x) functions as activation functions of the hidden layer and output layer, respectively. Finally, the classical optimization and collocation methods are applied to train this neural network in first and second methods, respectively. In addition, to show the accuracy and efficiency of the current techniques, we test those on various types of Lane–Emden equations and our schemes are compared with some other numerical methods.