High-accuracy prediction of Kβ/Kα intensity ratios via explainable stacked-ensemble learning: A web-based...

The Kβ/Kα intensity ratios are critical parameters that quantitatively characterize atomic shell transition dynamics and radiative branching probabilities. In this study, we systematically evaluated the capability of machine learning (ML) algorithms to predict these ratios, as well as their advantages over traditional theoretical models (such as Scofield and semi-empirical calculations). A large dataset comprising 2124 experimental measurements compiled from the literature, covering elements with atomic numbers (Z) from 11 to 96, was structured to include more than ten variables, such as atomic number, sample form, excitation source, detector type, and energy resolution. Missing observations were imputed using the multivariate imputation by chained equations (MICE) method in the R programming language. Categorical variables were one-hot encoded, and the data were split into an 80% training set and a 20% test set. Seven heterogeneous individual models (RF, XGBoost, Cubist, SVR, GPR, BRNN, and GLMNET) were constructed, along with seven different stacking combinations derived from them. Following 10×10-fold cross-validation, the highest accuracy was achieved by the stacked model using a BRNN meta-learner (RMSE = 0.009; R² = 0.973). This model reduced the test error of the Scofield theory by nearly 48% and performed significantly better according to the Diebold-Mariano test (p < 0.001). SHAP analysis revealed that atomic number is the primary determinant, while sample purity and excitation source have secondary yet physically consistent effects. Furthermore, an online R/Shiny-based calculator enhances the practical applicability of the method by enabling users to input their experimental parameters and receive instantaneous Kβ/Kα predictions. These results demonstrate that at the current stage of theoretical and experimental development, data-driven approaches provide significant advantages in both accuracy and interpretability over classical theories for complex atomic parameters such as the Kβ/Κα intensity ratio. Overall, this work constitutes a significant step toward reducing deviations in high-Z elements, improving detector calibration, and establishing new atomic databases.