Hybrid analytical–ANN modeling of ferroconvection with couple stresses under variable gravity fields

This study investigates the effect of couple stresses on ferroconvection under three cases of variable gravity- z , − z , and z 2 . To determine the stability thresholds both linear and nonlinear approaches are used. Linear stability is evaluated using the normal mode method, while nonlinear stability is examined through the energy method, incorporating a generalized energy function. The eigenvalue problems are solved using the Galerkin method. The results reveal the effects of magnetization, couple stresses, and variable gravity on the onset of convection and the extent of the subcritical region, as indicated by the differences between linear and nonlinear Rayleigh numbers. Also, the study reveals that directional variations in gravity can either stabilize or destabilize the system. To enhance computational efficiency and facilitate rapid stability predictions, a multi-output artificial neural network (ANN) model is developed using data generated from these mathematical expressions. The ANN effectively learns the complex parametric dependencies of the Rayleigh numbers, enabling near-instantaneous stability assessment without re-evaluating the full analytical expressions. The findings advance the understanding of ferroconvection under complex physical conditions and establish ANN as a scalable and efficient tool for real-time stability assessments. • Developed nonlinear stability model for ferroconvection with variable gravity. • Built ANN to predict critical Rayleigh numbers across broad parameter ranges. • Integrated mechanics and machine learning for fast scalable ferrofluid modeling.