Onset of convection in a rotating bi-dispersive porous medium using analytical and machine learning methods: linear stability analysis and classification

Abstract We investigate the onset of double-diffusive convection in a rotating bi-dispersive porous medium (BDPM) saturated with an electrically conducting fluid and subjected to an external magnetic field. The BDPM is heated from below, giving rise to onset of convection and is rotated about a vertical axis with a uniform angular velocity. Using linear stability analysis, we derive critical thermal and concentration Rayleigh numbers for both steady and oscillatory convection modes, systematically examining the effects of key dimensionless parameters such as the Vadasz number, Taylor number, magnetic parameter and others. To enhance predictive capabilities, we implement a supervised machine learning framework. A Support Vector Machine (SVM) with a radial basis kernel and an Artificial Neural Network (ANN) are trained on analytically generated data to accurately classify steady and oscillatory convection regimes, achieving 97.33% accuracy. It is demonstrated that magnetic damping, rotational restraint, and thermal coupling collectively suppress oscillatory convection, promoting stability. We have also performed a data-driven optimization to identify parameter combinations that suppress oscillatory convection. By minimizing the probability of oscillatory behavior from the SVM model, we obtain optimal physical conditions corresponding to the most stable regime.