# An Interpretable XGBoost Framework for Predicting Oxide Glass Density
## 5 Conclusions  
This study developed and validated a machine learning framework for the accurate prediction of oxide glass density. It was unequivocally demonstrated that the predictive power of the models is dependent on the physical and chemical sophistication of the input features, with performance improving hierarchically from simple compositional data to advanced, physically informed descriptors. The coefficient of determination (R\({}^{2}\)) ranged from 0.77 for a simple linear model with purely compositional features to 0.97 for the eXtreme Gradient Boosting (XGBoost) model combined with the comprehensive Magpie feature set. This optimal model achieved a low mean percentage error of 2.2%, showing its high accuracy.  
The significant contribution of this work is the insight gained from model interpretability. Feature importance and SHAP analysis revealed that the algorithm learned to approximate the fundamental physical principles governing density. The model autonomously identified the mean atomic weight as a direct proxy for molar mass (M) and utilized features describing electronic structure to approximate the molar volume (V\({}_{\text{m}}\)), effectively mirroring the physical density equation. This confirmation that the model buildsa scientifically valid framework, rather than merely fitting to correlations, is crucial for establishing trust in data-driven methods.  
However, the study has limitations, most notably the model's reduced accuracy for higher-density glasses, which are less prevalent in the training data. Future research will aim to address this by exploring advanced sampling and reweighting techniques. Furthermore, while the current work successfully predicts density from composition alone, another promising direction involves incorporating explicit structural descriptors, such as the fraction of bridging and non-bridging oxygens, to build even higher-fidelity models for more specialized datasets.  
The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app15158680/s1](https://www.mdpi.com/article/10.3390/app15158680/s1)]([https://www.mdpi.com/article/10.3390/app15158680/s1](https://www.mdpi.com/article/10.3390/app15158680/s1)): Table S1: Compositional features; Table S2: Atomic types features; Table S3: Meredig features; Table S4: Mageite features; Table S5. Values of the tuned hyperparameters (the rest of the parameters were set as their default values in Scikit-learn); Table S6. Percentage error statistics.  
This research was funded by the subsidy of the Ministry of Science and Higher Education for the AGH University of Krakow, project No 16.16.160.557.  
The original code and data used in the study are openly available in Rodbuk AGH repository at [[https://doi.org/10.58032/AGH/WY0](https://doi.org/10.58032/AGH/WY0) GEJ]([https://doi.org/10.58032/AGH/WY0](https://doi.org/10.58032/AGH/WY0) GEJ).  
Research project supported by the program \"Excellence initiative--research university\" for the AGH University of Krakow.  
The author declares no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.  
The following abbreviations are used in this manuscript: