Novel design of nonlinear autoregressive with exogenous noise-based intelligent networks for dynamics of MHD Casson–Williamson models involving heat generation and viscous dissipation

Abstract

In the current arena, the role of artificial intelligence (AI) has gained immense impact in the field of computational fluid dynamics (CFD) due to mesh improvement efficiency, optimal manual intervention, reliable forecasting, comprehending data analytic decisions, and utilization of machine automation. The study under investigation treatise on CFD problem representing the flow of Casson and Williamson fluids (CWFs) model with heat generation and viscous dissipation by using AI-based knacks through nonlinear autoregressive exogenous (NARX) networks backpropagated with Bayesian regularization technique (BRT), i.e. NARX-BRT. The design NARX-BRT procedure implemented on data generated with Adams numerical scheme for CWFs by carefully altering parameters i.e. Darcy number, Casson fluid, mass convective Williamson, mixed convection, thermal conductivity, thermal convective, and Eckert number, with fixed values Prandtl and Schmidt numbers. Results invariably matched with the reference/standard numerical solutions for the CWF model having significantly reduced magnitude of error for each anticipated CWF scenario. The effectiveness of projected CWF is portrayed exhaustively through mean square error (MSE) based iterative learning curves, analysis of adaptive controlling factors, error histogram plots, and regression metrics for variants of nonlinear differential order systems of CWF-based CFD.