Prediction of wave reflection coefficient in coastal structures using machine learning and stacking models

In this study, various machine learning (ML) algorithms and the Stacking Regressor (SR) method were utilized to predict the wave reflection coefficient (Kr) for breakwaters and coastal structures. Using Random Forest (RF), Extra Trees (ET), Extreme Gradient Boosting (XGB), Light Gradient Boosting Machine (LGBM), CatBoost (CAT), and Histogram Gradient Boosting (HGB) algorithms, 20 different SR models were developed, and hyperparameter optimization was conducted using the Optuna framework. The Mutual Information (MI) technique was applied for feature selection, identifying 12 out of 18 parameters as the most influential. During model training, the Root Mean Square Error (RMSE) served as the loss function, and performance was evaluated using R 2 , Willmott Index (WI), MSE, and RMSE metrics. Among the base models, the ET algorithm achieved the highest predictive accuracy (R 2 = 0.932, RMSE = 0.048). The best stacking configuration, combining ET, XGB, and HGB, produced similarly high accuracy (R 2 = 0.926, RMSE = 0.049) with fewer large-error instances and greater generalization stability. Overall, SR-based ML frameworks offer robust, interpretable, and computationally efficient alternatives to Artificial Neural Networks (ANNs), providing reliable and balanced estimations of Kr for practical wave–structure interaction applications. • K r values were predicted with high accuracy using ML and symbolic regression methods. • The MI method selected the 12 most influential input parameters for model training. • SR models outperformed baseline algorithms with lower absolute errors.