Accelerated prediction of three-dimensional MHD mixed bioconvection using hybrid finite element–XGBoost–CatBoost framework in a porous square cavity with a bended obstacle

Motivated by the need to enhance heat and mass transfer control in complex porous thermal systems, this study investigates three-dimensional magneto-bioconvection in a ferrofluid-filled enclosure containing a quarter-torus obstacle. The coupled momentum, energy, concentration and microorganism transport equations have been solved numerically through the finite element method and XGBoost and CatBoost models have been constructed to predict the Nusselt number, Sherwood number, and motile microorganism transport rate. The influence of the Hartmann number, Peclet number, Darcy number and the inclination angle of the magnetic field are studied and found that the Nusselt number is reduced from 1.12096 to 0.871687 with decreasing Darcy number from 10 −3 to 10 −5 . This demonstrates the significant effect of porous resistance on the heat transfer coefficient. A higher Hartmann number also suppresses convection by the Lorentz force, and a higher Peclet number has a very strong effect on the transport of microorganisms. All machine-learning models can produce the FEM result with a high level of accuracy, with R 2 > 0.998 being obtained for all the predicted quantities, and the CatBoost model performs best overall. The proposed FEM–machine-learning framework is an efficient way of predicting the coupled heat, mass, and bioconvective transport, and it has potential applications in magnetically controlled cooling, porous heat exchangers, energy-conversion devices, compact thermal management systems, and bio-thermal transport technologies.