Hybrid Machine Learning-Based Approach for Predicting the Poisson's Ratio of Mechanical Metamaterials

Abstract

This study proposes and validates a framework that integrates Grey Wolf Optimization (GWO) with Extreme Gradient Boosting (XGBoost) for estimating the Poisson's ratio of auxetic structures. First, for 320 models derived from Computer-Aided Design-based (CAD-based) unit-cell designs, a systematic sweep of diameter and cellular dimensions was conducted to obtain porosity coverage in the 45-85% range. Subsequently, elastic modulus and Poisson's ratio were computed via finite element analysis (FEA) at three mesh resolutions (0.20/0.25/0.30 mm), and relationships between design variables and outputs were examined using correlation heatmaps and Locally Weighted Scatterplot Smoothing (LOWESS) curves. GWO optimized the XGBoost hyperparameters through a multi-band narrowed search strategy; performance was evaluated using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Squared Error (MSE), and Coefficient of Determination (R2) metrics, as well as residual diagnostics and Ground Truth-Prediction alignments for Poisson's ratio. Across all configurations, R2 >= 0.994 and absolute errors are on the order of similar to 10-3; the 0.25 mm mesh stands out in terms of overall balance with the lowest squared-error profile and the highest R2, the 0.30 mm mesh is practically equivalent in terms of MAE, and the 0.20 mm mesh is comparatively weaker. Residual diagnostics-comprising a pattern-free cloud around zero, slight right-skewness, and limited heteroskedasticity-indicate low bias and no substantive model-specification issues. The findings align with physical insight, confirming that Poisson's ratio shifts toward more negative values as porosity increases and toward less negative values as diameter increases. The proposed GWO-XGBoost framework provides a reliable pre-screening tool for rapid design exploration and Poisson's-ratio-targeted optimization, with the potential to reduce the need for additional FEA simulations and experimental iterations during early-stage design.