Numerical and intelligent neuro-computational modelling with Fourier’s energy and Fick’s mass flux theory of 3D fluid flow through a stretchable surface

Current work explores the intricacies of magnetohydrodynamic and mix convectional boundary-layer flow concerning couple stress Casson nanofluid (CSCNF) dynamics via a 3D stretchable surface. The addition of active and passive control mechanisms for nanoscales creates an innovative dimension to the exploration. Remarkably, the analysis incorporates the influence of non-Fourier and non-Fickian heat and mass flux, alongside the effects of thermophoresis and Brownian diffusion, to systematically investigate the heat and mass transportation phenomena. The governing equations (PDEs) describing the MHD-3DCSCNF model are converted into a set of ordinary differential equations to facilitate the ANN analysis. Employing the bvp4c technique, a dataset is systematically generated for the back propagation artificial neural network with Levenberg–Marquardt Algorithm (BANN-LMA) through four distinct scenarios. Via accurate testing, validation, and training, the BANN-LMA produces estimated results for the MHD-3DCSCNF problem. The performance validation of BANN-LMA is executed through several metrics, involving the mean squared error, error histogram and regression analysis. The training process, characterized by minimizing the MSE through a gradient descent methodology with optimized weights, exhibits a compelling correlation R = 1, between the target and network output. Furthermore, the consistent convergence observed highlights the method robustness and reliability.