Bayesian regularization neural network analysis of heat and mass transfer in hybrid nanofluid flow over a lubricated stretching sheet with power-law lubricant layer and magnetic field effects

• A Bayesian Regularization Neural Network (BRNN) is implemented for the first time to predict and analyze hybrid nanofluid flow behavior over a lubricated stretchable surface, demonstrating superior accuracy and generalization compared to traditional numerical schemes. • The combined effects of magnetic field strength , power-law rheology , nanoparticle concentration , Brownian motion , thermophoresis , and temperature-dependent thermal conductivity are systematically examined to reveal their interplay in modifying flow, heat, and mass transfer characteristics. • Findings indicate that the power-law lubricant layer and magnetic induction synergistically enhance heat transfer and minimize flow resistance, optimizing lubrication performance under magneto-thermal conditions. • The BRNN results show strong agreement with the Legendre Wavelet-Based Spectral Collocation Method (LW-SCM), confirming the stability and robustness of the proposed neural network model. • The outcomes demonstrate that neural network-based predictive modeling of hybrid nanofluids can significantly contribute to micro-lubrication, energy conversion, and thermal management technologies, offering pathways for intelligent thermal system design. Hybrid nanofluids have lately received extensive interest due to its excellent lubrication and heat transfer properties in engineering. In this paper, a Bayesian Regularization Neural Network (BRNN) analysis of the thermal and material transport in the hybrid nanofluid flow through a lubricated stretchable surface with a power-law lubricant layer under the impacts of a magnetic field is conducted. The study will be motivated on the joint role of magnetic field magnitude, power-law rheological behavior, nanoparticle concentration, Brownian motion, thermophoresis, and temperature-dependent thermal conductivity on the velocity, temperature, and concentration patterns in the flow. Governing equations that describe the continuity of mass, momentum, energy, and concentration, and interfacial shear stress continuity, as well as slip/no-slip boundary conditions, are used to indicate realistic physical behavior. The BRNN approach to solving the nonlinear coupled equations gives stable and accurate solutions with a high level of generalization and is checked against the Legendre Wavelet-Based Spectral Collection Method (LW-SCM). The computed outcomes imply that power-law lubricant and magnetic induction can be applied readily to increase the thermal energy transfer and decrease flow resistance, and the inclusion of nanoparticles can increase thermal transmission rate and save energy. This study’s results have shown that neural network-based methods can be used to model complex hybrid nanofluid systems and bear practical implications in micro-lubrication and thermal management, and energy conversion technologies.