Hybrid Galerkin-machine learning framework for fluid-structure interaction and stability of immersed moving FG-CNTRC microplates under multiphysics effects

Purpose This study aims to develop a hybrid Galerkin-machine learning (ML) framework for the rapid and accurate prediction of the vibration characteristics and stability boundaries of bidirectionally moving functionally graded carbon nanotube-reinforced composite (FG-CNTRC) microplates immersed in a confined fluid under coupled multiphysics effects, including hygrothermal loading, non-uniform in-plane forces and fluid-structure interaction. Design/methodology/approach The governing equations are formulated using strain-gradient elasticity and incompressible potential-flow theory with rigid-wall boundary conditions. The Galerkin method is used to discretize the governing equations, and the resulting complex eigenvalue problem is solved to determine natural frequencies, damping ratios and stability thresholds. A high-fidelity numerical database is subsequently generated to train three ML surrogate models, namely, decision tree (DT), random forest (RF) and least-squares boosting (LSBoost). Their predictive performance is evaluated using statistical error metrics together with parity plots, Bland–Altman analysis, error histograms and Taylor diagrams. Findings Among the developed surrogate models, LSBoost achieves the highest predictive accuracy, reducing the prediction error by approximately 45% compared with the best-performing RF model and by more than 60% relative to the fine DT model. The results further demonstrate that the FG-X distribution provides the greatest stability margin, whereas increasing fluid density, thermal loading, hygroscopic effects and bidirectional motion progressively reduce microplate stability. Once trained, the surrogate models provide near-instantaneous predictions, substantially reducing the computational cost associated with repeated eigenvalue analyses. Originality/value This study presents a novel hybrid computational framework that integrates Galerkin-based eigenvalue analysis with ML surrogate modeling for efficient prediction of the vibration characteristics and stability boundaries of fluid-interacting moving FG-CNTRC microplates under coupled multiphysics conditions. By combining high-fidelity physics-based modeling with data-driven surrogate learning, the proposed framework enables rapid parametric analysis and stability assessment while preserving the predictive accuracy of the underlying numerical model.