Numerical treatment for nonlinear MHD Jeffery-Hamel problem using neural networks optimized with interior point algorithm

In this paper new computational intelligence techniques have been developed for the nonlinear magnetohydrodynamics (MHD) Jeffery-Hamel flow problem using three different feed-forward artificial neural networks trained with an interior point method. The governing equation for the two-dimensional MHD Jeffery-Hamel flow problem is transformed into an equivalent third order nonlinear ordinary differential equation. Three neural network models using log-sigmoid, radial basis and tan-sigmoid activation functions are developed for the transformed equation in an unsupervised manner. The training of weights of each neural network is carried out with an interior point method. The proposed models are evaluated on different variants of the Jeffery-Hamel problem by varying the Reynolds number, angles of the walls and the Hartmann number. The accuracy, convergence and effectiveness of the designed models are validated through statistical analyses based on a sufficiently large number of independent runs. Comparative studies of the proposed solutions with standard numerical results, as well as recently reported solutions of analytic solvers illustrate the worth of the proposed solvers.