This study focuses on the thermally magnetized peristaltic propulsion of ternary hybrid nanofluids (TMPP-THNF) flowing through an asymmetric curved channel. The ternary hybrid nanofluids consist of aluminum oxide \(\left( {Al2O_{3} } \right)\) , zinc oxide \(\left( {ZnO} \right)\) and titanium dioxide \(\left( {TiO_{2} } \right)\) nanoparticles dispersed in the conventional base fluid distilled water \(\left( {H_{2} O} \right).\) Additionally, the effects of thermal radiation, Hall current, velocity slip, Ohmic heating, an applied magnetic field, heat dissipation, thermal boundary conditions, and heat sink/source are considered. A set of coupled nonlinear partial differential equations (PDEs) are derived from the model established in this study. The PDEs are initially transformed into dimensionless ordinary differential equations (ODEs) by applying biological constraints such as creeping transport and lubrication theory and dimensionless flow quantities. The simplified system is solved numerically using the NDSolve function. The Levenberg–Marquardt algorithm within a Backpropagation Neural Network (LMA-BNN) framework is designed to address the nonlinear characteristics and computational challenges associated with the suggested fluid flow model. This study introduces an innovative approach to develop a machine learning-enhanced numerical solver that employs the LMA-BNN approach. An ANN trained with the LMA is used to accurately and rapidly learn from numerical data, thereby predicting flow and thermal fields. The ANN-based methodology provides enhanced computational efficiency relative to traditional numerical approaches. The outcomes reveal that the transfer of heat performance is improved with augmentations of the Hartmann number, volume fraction of aluminum oxide nanoparticles, thermal slip, heat generation and curvature parameters. In addition, raising the volume fraction of nanoparticles improved heat transfer by 11.57%. The reliability and effectiveness of the LMA-BNN model are validated using error histograms, performance plots, regression analysis, state transition and time series plots. Evaluations were performed using the Mean Squared Error (MSE) criterion, which was found to be in the range of \(10^{ - 11}\) to \(10^{ - 10}\) , therefore indicating the high accuracy and stability of the proposed approach as a surrogate model.
