Eigenvalue-Consistent PI-ANN–GPR Surrogate Framework for Natural Frequency Prediction of Functionally Graded Hybrid Laminated Composite Plates

This study develops an eigenvalue-consistent physics-informed ANN–GPR hybrid surrogate framework for free-vibration prediction of functionally graded GPL/fiber-reinforced laminated composite plates under thermal conditions. High-fidelity reference natural frequencies and mode shapes are generated using a higher-order zigzag theory finite element model, while the temperature-dependent effective material properties are evaluated through modified Halpin–Tsai micromechanical homogenization and fiber-based mixture rules. Standard ANN, Gaussian process regression, physics-informed ANN, and four PI-ANN–GPR hybridization strategies are compared, including residual correction, latent-feature correction, parallel ensemble fusion, and multi-fidelity learning. The PI-ANN embeds vibration-specific physics through stiffness–mass eigenvalue consistency, thermomechanical monotonicity, reinforcement-induced stiffness trends, modal admissibility, and grading smoothness constraints. GPR is then used to correct residual frequency errors and quantify predictive uncertainty. The results show that the hybrid models significantly improve accuracy, error compactness, physical consistency, and extrapolation robustness compared with standalone ANN, GPR, and PI-ANN models. The latent-feature PI-ANN–GPR scheme provides the best overall performance, achieving a testing (R2) of 0.981 with MAE, MAPE, and RMSE values of 0.91%, 1.08%, and 1.24%, respectively. Computational analysis further demonstrates speedups of several orders of magnitude over repeated HOZT–FEM simulations. The proposed framework offers an accurate, uncertainty-aware, and computationally efficient tool for vibration-safe design, parametric studies, and optimization of advanced hybrid laminated composite structures.