Stability of thermal convection in rotating porous medium with heterogeneity under gravity modulation: Heat transfer via artificial neural network

In this paper, our aim is to investigate the effect of gravity modulation on thermal convection in a rotating horizontal porous medium with vertical heterogeneity. A machine learning technique is employed to numerically compute and predict the heat transfer rate under constant, linear, quadratic, and exponential heterogeneity models. Both linear and weakly nonlinear stability analyses are conducted to determine the onset of convection under the combined influence of vertical heterogeneity, Coriolis force, and gravity modulation. The critical Darcy–Rayleigh number is obtained using the Galerkin method, revealing that rotation and vertical heterogeneity significantly affect the stability thresholds. Furthermore, a feedforward artificial neural network (ANN) approach is developed to predict the Nusselt number, enabling a data-driven assessment of nonlinear heat transport across varying physical parameters. The ANN is trained and validated using numerical data derived from the weakly nonlinear analysis, demonstrating high prediction accuracy and strong generalizability. The key novel findings are as follows: (1) the Taylor number exhibits a stabilizing effect on the system, promoting stationary convection and (2) gravity modulation suppresses convection at higher modulation frequencies while enhancing heat transfer at lower frequencies. This hybrid analytical and ANN approach provides a robust framework for analyzing complex convective phenomena in a porous medium.