Hybrid ANN-GPR machine learning surrogate for dynamic behavior of functional materials

Modeling bidirectional functionally graded (BDFG) plates is challenging due to the continuous spatial variation of material properties. This study presents a novel machine learning (ML)-assisted isogeometric analysis (IGA) framework to predict the free vibration response of BDFG plates efficiently. The training dataset is generated using zigzag theory within an IGA framework, capturing high-fidelity structural behavior. Three regression-based ML algorithms—Gaussian Process Regression (GPR), Artificial Neural Network (ANN), and hybrid models (GA-optimized ANN and Bayesian-optimized GPR)—are employed. Additionally, a novel hybrid ANN-GPR model is proposed, where ANN extracts high-level features from raw input data, and GPR performs regression with uncertainty quantification. Further, an ANN-learned kernel replaces the conventional GPR kernel, enabling latent-space transformation for enhanced predictive performance. The proposed hybrid approach demonstrates superior computational efficiency and accuracy compared to standalone and optimized ML models, making it a robust tool for the analysis of BDFG structures.