A hybrid linear regression and CatBoost model for high-performance nonlinear static analysis of functionally graded plates

Abstract

Nonlinear static analysis of functionally graded material (FGM) plates using high-fidelity numerical methods such as Isogeometric Analysis (IGA) is computationally demanding because it requires iterative solution procedures to trace the equilibrium path. Recently, deep learning surrogates (e.g., Long Short-Term Memory, LSTM) have been explored to reduce repeated simulations; however, they can still require nontrivial training effort and careful model tuning. This study proposes a high-performance hybrid surrogate model combining Linear Regression (LR) and CatBoost to predict the nonlinear load-deflection behavior of FGM plates. The equilibrium-path response is formulated as a sequence regression task along pseudo-time load steps and decomposed into two stages: LR captures the global linear trend, while CatBoost learns the nonlinear residual component not represented by LR. The proposed approach is trained and validated using IGA-generated datasets. It is evaluated under different data-availability settings (30%, 50%, and 80% of the equilibrium-path sequence used for training and testing) and assessed in terms of prediction accuracy, hyperparameter sensitivity, and end-to-end computational cost (training + prediction). In our implementation, the combined LR-CatBoost training and prediction time is approximately 0.25 s for the baseline case, excluding the IGA computation required to generate the initially available response segment. Prediction accuracy is high, with mean absolute percentage errors on the order of 10^-2 to 10^-1% depending on the case. These findings indicate that the proposed LR-CatBoost strategy provides a robust and ultra-fast surrogate for near-real-time nonlinear structural analysis of FGM plates.