ANN-based prediction of radiative MHD casson blood-based hybrid nanofluid flow over a stretching sheet for biomedical applications: Stability and multiple linear regression approaches

This research investigates the Magnetohydrodynamic (MHD) flow, heat transfer, and stability characteristics of an Au–Cu hybrid nanofluid over a permeable stretching sheet, incorporating Casson blood as the base fluid. The mathematical framework integrates the effects of magnetic fields, thermal radiation, heat generation, Darcy resistance, and non-Newtonian rheological properties. The governing nonlinear boundary-layer equations are transformed into a system of ordinary differential equations and subsequently solved numerically utilizing the MATLAB bvp4c solver. Two numerical experiments, specifically mesh-sensitivity and domain-independence tests, are conducted to evaluate numerical accuracy, complemented by a temporal stability analysis to assess the stability of the derived numerical solutions. An artificial neural network (ANN) is subsequently trained to serve as a numerical surrogate for these solutions. In addition to conventional ANN assessment metrics, the magnetic parameter M is evaluated through an independent case-wise validation to rigorously assess generalization capability, ensuring the absence of point-wise leakage from the target profile being validated. For this extra evaluation, 8 complete velocity profiles (8000 spatial samples) are taken into account, distributed into 6 velocity profiles for training (6000 spatial samples), 1 profile for validation (1000 spatial samples), and the whole profile for M = 3 . 1 is solely used for the independent test (1000 spatial samples). The ANN achieves R 2 = 0 . 9 9 9 8 7 , R M S E = 1 . 7 1 0 7 × 1 0 − 3 , and M S E = 2 . 9 2 6 5 × 1 0 − 6 ) , demonstrating close agreement with the BVP4C reference solution for an unseen value of M within the investigated range. Multiple linear regression is further employed to characterize specific parameter-response relationships, although the limited scale of the internal dataset constrains the interpretability of these findings. The results demonstrate that the magnetic field inhibits velocity while enhancing temperature, and Darcy resistance conversely reduces velocity. The maximum wall heat transfer magnitude is recorded for the hybrid suspension, relative to pure blood, Au/blood, and Cu/blood suspensions. These findings remain theoretical and necessitate experimental validation prior to their implementation in biomedical applications.