The prediction of frequency band-gaps for Green-Naghdi (GN)-based thermoelastic wave propagation within graphene platelets (GPLs)/carbon nanotubes (CNTs)-reinforced phononic crystals (PnCs) is a complex and crucial task for advancing the design and optimization of these materials. This paper presents hybrid machine learning-based methods with transfer matrix method (TMM) for predicting the frequency band-gaps of GN-based thermoelastic wave propagation in GPLs/CNTs-reinforced PnCs. Specifically, five hybrid machine learning algorithms are proposed as TMM-RFR, TMM-LR, TMM-KNN, TMM-MLP, and TMM-XGBoost, which are based on TMM and random forest regression (RFR), linear regression (LR), K-nearest neighbors (KNN), multi-layer perceptron (MLP) and extreme gradient boosting (XGBoost) algorithms, respectively. The required data for training algorithms are obtained using the transfer matrix method (TMM). Each model is trained using a set of features derived from the material properties of the GPLs/CNTs-reinforced PnCs. The performances of the proposed hybrid models are quantitatively assessed using three common error metrics: root mean squared error (RMSE), mean absolute error (MAE), and the coefficient of determination (R²). Through this study, we aim to identify the most effective TMM-based hybrid machine learning technique for predicting the frequency band-gap, offering insights into the trade-offs between prediction accuracy and model complexity. The results highlight the strengths and weaknesses of each method, providing valuable guidance for future research and engineering applications involving the design of the GPLs/CNTs-reinforced PnCs and other advanced metamaterials. Also, effects of the GPLs/CNTs volume fractions on the frequency band-gaps of thermoelastic wave propagation have been obtained using TMM-XGBoost as the desired TMM-based hybrid machine learning method and discussed in details for a GPLs/CNTs-reinforced PnCs.

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