Dynamics of three-point boundary value problems with Gudermannian neural networks

• Published in: Evolutionary intelligence Vol. 16; no. 2; pp. 697 - 709
• Main Authors: Sabir, Zulqurnain, Ali, Mohamed R., Raja, Muhammad Asif Zahoor, Sadat, R., Baleanu, Dumitru
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Artificial Intelligence; Bioinformatics; Boundary value problems; Computation; Control; Convergence; Engineering; Genetic algorithms; Mathematical and Computational Engineering; Mechatronics; Neural networks; Research Paper; Robotics; Stability analysis; Statistical Physics and Dynamical Systems; Active-set method; Numerical computing; Singular three-point models; Gudermannian kernel; Artificial neural networks; Genetic algorithms
• ISSN: 1864-5909; 1864-5917
• DOI: 10.1007/s12065-021-00695-7

The present study articulates a novel heuristic computing design with artificial intelligence algorithm by manipulating the models with Feed forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of Genetic algorithms (GA) combined with rapid local convergence of Active-set method (ASM), i.e., FF-GNN-GAASM for solving the second kind of Three-point singular boundary value problems (TPS-BVPs). The proposed FF-GNN-GAASM intelligent computing solver integrated into the hidden layer structure of FF-GNN systems of differential operatives of the second kind of STP-BVPs, which are linked to form the error based Merit function (MF). The MF is optimized with the hybrid-combined heuristics of GAASM. The stimulation for presenting this research work comes from the objective to introduce a reliable framework that associates the operational features of NNs to challenge with such inspiring models. Three different measures of the second kind of TPS-BVPs is applied to assess the robustness, correctness and usefulness of the designed FF-GNN-GAASM. Statistical evaluations through the performance of FF-GNN-GAASM is validated via consistent stability, accuracy and convergence.