Dynamics of Darcy–Forchheimer flow of Casson nanofluidic model with Newtonian heating: Nonlinear input–output neural networks

This research work presents the numerical solution of the Darcy–Forchheimer flow of Casson nanofluidic model (DFFCNFM) on stretching sheets with Newtonian heating by utilizing a combination of nonlinear input–output neural networks with backpropagation of Levenberg–Marquardt computational approach. The presented study investigates the impact of electroosmosis forces on the boundary layer of the Casson nanofluid, focusing on viscous and Joule dissipations. A dataset for DFFCNFM is generated for the different events with backward differentiation formula (BDF) by varying Casson fluid parameter ([Formula: see text], permeability parameter (Da), electric parameter ([Formula: see text], Reynolds number (Re) relative to stretching velocity, magnetic field ([Formula: see text], Eckert number (Ec), and Prandtl number (Pr). The artificial intelligence-inspired technique via nonlinear input–output neural networks with backpropagation of Levenberg–Marquardt is utilized from the generated dataset for DFFCNFM to find the approximate solutions. The satisfactory performance levels, as indicated by the mean square error (MSE), have been attained consistently with magnitude around 10[Formula: see text]–10[Formula: see text] for all scenarios of DFFCNFM. The precision and performance validation is effectively established by the negligible MSE, close proximity to the unit value of regression metric, and the distribution of instances in error-histograms.