Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models

Kashif Nisar,Ag Asri Ag Ibrahim,Manoj Gupta,Adnan Shahid Khan,Muhammad Asif Zahoor Raja,Danda B Rawat,Aldawoud Kamal,Zulqurnain Sabir,Joel J P C Rodrigues

doi:10.3390/app11114725

Abstract

In this work, a new heuristic computing design is presented with an artificial intelligence approach to exploit the models with feed-forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of genetic algorithms (GA) combined with local convergence aptitude of active-set method (ASM), i.e., FF-GNN-GAASM to solve the second kind of Lane–Emden nonlinear singular models (LE-NSM). The proposed method based on the computing intelligent Gudermannian kernel is incorporated with the hidden layer configuration of FF-GNN models of differential operatives of the LE-NSM, which are arbitrarily associated with presenting an error-based objective function that is used to optimize by the hybrid heuristics of GAASM. Three LE-NSM-based examples are numerically solved to authenticate the effectiveness, accurateness, and efficiency of the suggested FF-GNN-GAASM. The reliability of the scheme via statistical valuations is verified in order to authenticate the stability, accuracy, and convergence.

Highlights

IntroductionThe singular models have many appreciated applications in physics, physiology, engineering, and mathematics
The basic aim of this study is to solve the second kind of Lane–Emden nonlinear singular models (LE-NSM) by introducing a new intelligent scheme based on combined heuristics of Gudermannian neural networks (GNN)-GAASM
The current research work is related to design a novel Gudermannian neural network for solving the nonlinear Lane–Emden singular model of the second kind using GNNGAASM containing the singular point at the origin using 10 neurons

Summary

Introduction

The singular models have many appreciated applications in physics, physiology, engineering, and mathematics. The paramount Lane–Emden model is a historical model, which is famous due to singularity and presented by Lane and Emden [1,2] a few centuries ago by working on the performance of thermal gas and the state of thermodynamics [3]. The generic form of the Lane–Emden nonlinear singular models (LE-NSM) is written as [4]: creativecommons.org/licenses/by/ 4.0/).

Objectives

Methods

Conclusion