# An Interpretable XGBoost Framework for Predicting Oxide Glass Density
## 4 Discussion
Lead is the most important element increasing glass density. This effect stems from its very high atomic mass. Lead glasses are a classic example of high-density materials with a high refractive index. The model correctly identified this dominant effect. High proportions of Na, K, Li, and Ca (red dots) have predominantly negative SHAP values. The addition of these elements lowers the predicted density. These lightweight modifiers build into the glass network voids, but they also cause it to \"loosen\" and break the oxygen bridges (Si-O-Si), leading to an increase in the so-called free volume and, consequently, a decrease in density compared to pure, network-forming glasses. Aluminum has a complex effect, but generally, its high content slightly lowers density. As an intermediate element, its role depends on the rest of the composition. Barium is a heavier modifier (compared to Ca or Na), and its high content (red dots) biases the prediction toward higher density (positive SHAP), consistent with its high atomic mass. A closer inspection of the feature importance results reveals an insightful discrepancy between the different metrics, particularly for the model using Compositional features. The most prominent example is the oxygen fraction, which ranks as the most important feature by weight (gain) due to its high abundance and frequent use in decision tree splits. However, its permutation importance is considerably lower than that of key cations like Pb, B, and Si. This distinction highlights the model's ability to learn nuanced physical roles; it correctly identifies that while the oxygen sublattice is structurally ubiquitous, the variation in glass density is overwhelmingly driven by the specific type of cations incorporated into the network. Notably, this discrepancy diminishes for the advanced Meredig and Magpie sets, where all importance metrics converge in identifying mean atomic weight as the dominant feature, aligning the model's internal logic with direct predictive impact. The error analysis further reinforces these findings while also highlighting the model's limitations. The progressive narrowing of the error distribution, with the average error decreasing from 4.4% to 2.2% when moving from Compositional to Magpie features, directly reflects the model's increased certainty and accuracy when working with better data representation. However, the consistent trend of increasing prediction error for higher-density glasses points to remaining challenges. This is likely due to a combination of factors, including a lower prevalence of such materials in the training dataset and the greater structural complexity of glasses containing heavy elements like lead, bismuth, or tellurium, which may not be fully captured even by the advanced techniques such as data reweighting, or the use of distribution-aware loss functions could potentially mitigate this imbalance. The implementation of such sampling and training strategies remains a valuable and promising direction for future work aimed at further optimizing the model's precision in this specific, high-density regime. Beyond refining the feature set with atomic-level properties, another way for enhancing predictive models involves incorporating explicit structural descriptors of the glass network, for instance, by using features derived from the atomic-level structure, such as the relative fractions of bridging oxygens (BO), non-bridging oxygens (NBO), and free oxygens (FO) [21]. Such models can capture nuances of the glass network topology that are only implicitly represented by compositional features, potentially leading to even higher prediction accuracy. Nevertheless, these structural features are not available in large experimental databases and must be calculated using computationally expensive methods, such as molecular dynamics simulations, for each composition. In conclusion, this work successfully demonstrates a data-driven methodology for the accurate prediction of glass density.