Stacking machine learning models for predicting hardness and modulus in refractory metal high-entropy nitride coatings

Refractory metal high-entropy nitride (RHEN) coatings have attracted significant attention for extreme environmental applications due to their outstanding mechanical properties. However, traditional trial-and-error methods for optimizing process parameters are inefficient and costly. To solve this limitation, this study proposes a stacking machine learning framework to predict the hardness and modulus of the RHEN coatings accurately. Seven heterogeneous algorithms, including Random Forest (RF) and XGBoost, were employed to construct base learners coupled with a meta-learner. The stacking model of hardness achieved a satisfactory accuracy (R² = 0.9011), which is 10 % higher than that of individual models. Additionally, the impact of each feature on the hardness and modulus was clarified using SHAP (Shapley Additive Explanations). The obtained stacking model was validated with experimental results. This result indicates that the stacking machine learning model is capable of enhancing the accuracy of individual models and precisely predicting the hardness and modulus of RHEN coatings.