Machine learning-based investigation of radiation and Soret–Dufour effects on magnetohydrodynamic Casson bioconvective flow

This work investigates the transport dynamics of Casson fluids over a vertically extending surface, a subject of great relevance in surface coatings, bioremediation, and biomedical engineering. Under these conditions, one must grasp how non-Newtonian behavior interacts with micro-level transportation systems. The main goal is to investigate Casson fluid's behavior under the combined influence of Soret and Dufour events, thermophoresis, Brownian motion, and microbiological convection. The main equations are simplified into a set of regular equations using similarity transformations, and then MATLAB's boundary value problem fourth-order collocation solver is used to find a numerical solution for this set. Although supporting flow (λ=0.5) lowers velocity near the wall, significant results show that raising the Casson parameter (β) increases flow rates. Thermal radiation significantly increases temperature distribution, while the Dufour effect enhances thermal transport but reduces concentration. In contrast, the Soret effect strengthens solute transfer by thickening the concentration boundary layer. Additionally, a multiple linear regression model, trained on numerically generated data, accurately predicts key outputs of skin friction, Nusselt number, Sherwood number and motile microorganism density number (R2 ≈ 0.98). The proposed numerical-statistical framework provides a comprehensive approach for modeling and predicting complex biothermal transports in non-Newtonian nanofluid systems.