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

• Main Authors: Kashif, Nisar, Zulqurnain, Sabir, Muhammad Asif Zahoor, Raja, Ag. Asri Ag., Ibrahim, Joel J. P. C., Rodrigues, Adnan, Shahid Khan, Manoj, Gupta, Aldawoud, Kamal, Danda B., Rawat
• Format: Article
• Language: English
• Published: MDPI 2021
• Subjects: QA75 Electronic computers. Computer science; QA76 Computer software
• Online Access: http://ir.unimas.my/id/eprint/35355/1/applsci-11-04725-v2.pdf; http://ir.unimas.my/id/eprint/35355/; https://www.mdpi.com/journal/applsci; https://doi.org/10.3390/app11114725

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.