Novel Deep Cascade Neural Network With Bayesian Regularization Backpropagation for Modeling of SWCNTs‐CuO/Ethylene Glycol Hybrid Nanofluids With Stretching and Shrinking Surfaces

ABSTRACT The objective of this study is to illustrate the mathematical behavior of hybrid nanofluidic model involving SWCNTs‐CuO/ethylene glycol as a base fluid using cascade forward neural network with Bayesian regularization technique (CFNNs‐BRT). The mathematical formulation of SWCNTs‐CuO/ethylene glycol with stretching and shrinking surfaces is portrayed by partial differential equations (PDEs), which are transformed into a system of nonlinear ordinary differential equations (ODEs) through suitable substitutions while the analysis is conducted for the physical parameter of interest such as unsteadiness, the constant stretching/shrinking, magnetic field, the mass flux constraint, temperature ratio, and the thermal radiation parameters. Synthetic dataset is created by Adams’ computing paradigm and the supervised methodology CFNNs‐BRT is implemented on the attained data, and the outcomes of CFNNs‐BRT reliably align with numerical solutions for each case of SWCNTs‐CuO/ethylene glycol that demonstrating with negligible error. The legacy of CFNNs‐BRT procedures is efficiently illustrated with mean squared error based learning curves, learn of adaptive controlling parameters, error frequency distribution bins, and regression studies for exhaustive experimentations for hybrid nanofluidic model involving SWCNTs‐CuO/ethylene glycol. According to the study, under stretching or shrinking surface circumstances, the hybrid SWCNT–CuO/ethylene glycol nanofluid may generate two potential solutions, but only within certain parameter constraints. It provides improvement in the primary branch and greater thermal conductivity than single‐particle nanofluids. While the secondary branch is unstable, stability checks reveal that the primary branch is both stable and physically reachable