Fig. 1. (a) Cross-validation coefficient of determination (R2) and (b) adjusted R2 ($R_{\text{adj}}^{2}$) of XGBoost regressor fed with subsets selected via EFS approach.

Fig. 2. Distribution of maximum casting diameter (Dmax) values in original dataset, and bulk metallic glasses whose Dmax values are greater than 8 mm form rare domain.

Fig. 3. (a) Data distributions of original training data and augmented training data by using the four augmentation techniques of SMOTE, SMOGN, OSIP, and OSGN. (b) Performance of XGBoost regressor model with original training data and the four data augmentation techniques.

Fig. 4. (a) R2 values of XGBR, RFR, ABR, SVR, and KNNR on OSGN data under cross-validation, and on testing data. (b) Grid search procedure of the weight of optimal XGBR (ωXGBR) in VR model, where model performance is assessed by average of CV-R2and testing R2.

Fig. 5. Predicted Dmax values with VR model are plotted against corresponding values (a) on whole OSGN training data, (b) on OSGN training data with ten-fold cross-validation (blue diamonds) and on testing data (green circles). Red diamond represents outlier Sc36Al24Co20Y20 under cross-validation.

Fig. 6. Ranked mean absolute SHAP (|SHAP|) values of six features fed into the voting regressor for predicting Dmax, darker features are more important than lighter ones.

Fig. 7. SHAP values of each OSGN datum of (a) average atomic radius $\bar{r}$, (b) feature Θ, (c) entropy of mixing Smix, and (d) enthalpy of mixing Hmix on predicting Dmax.