Unsupervised neural network model optimized with evolutionary computations for solving variants of nonlinear MHD Jeffery-Hamel problem

Abstract

A heuristic technique is developed for a nonlinear magnetohydrodynamics (MHD) Jeffery-Hamel problem with the help of the feed-forward artificial neural network (ANN) optimized with the genetic algorithm (GA) and the sequential quadratic programming (SQP) method. The two-dimensional (2D) MHD Jeffery-Hamel problem is transformed into a higher order boundary value problem (BVP) of ordinary differential equations (ODEs). The mathematical model of the transformed BVP is formulated with the ANN in an unsupervised manner. The training of the weights of the ANN is carried out with the evolutionary calculation based on the GA hybridized with the SQP method for the rapid local convergence. The proposed scheme is evaluated on the variants of the Jeffery-Hamel flow by varying the Reynold number, the Hartmann number, and the angles of the walls. A large number of simulations are performed with an extensive analysis to validate the accuracy, convergence, and effectiveness of the scheme. The comparison of the standard numerical solution and the analytic solution establishes the correctness of the proposed designed methodologies.