Quantifying oxide glass similarity through learned distances: a SHAP-based Earth Mover’s Distance

Quantifying how similar or different two glass compositions are is a central challenge with practical consequences for intellectual property, materials discovery, and database organization. Classical compositional distances — such as Euclidean or Manhattan metrics — treat all oxides as equally interchangeable, failing to capture the fact that substituting, e.g., Na 2 O for Li 2 O is chemically very different from substituting Na 2 O for CaO. In this work, we propose a framework that combines machine learning, SHAP (SHapley Additive exPlanations), and the Earth Mover’s Distance (EMD). Random Forest models were trained on compositions from SciGlass database to predict four key properties: glass transition temperature, thermal expansion coefficient, refractive index, and Young’s modulus. SHAP dependence curves were extracted for each oxide and each property, and the area between curves was used as a cost matrix reflecting how interchangeable two oxides are in their effect on a given property. This cost matrix defines an EMD between glass compositions. The resulting SHAP-EMD distance recovers chemical hierarchies that classical metrics miss, ranking substitutions of equal compositional magnitude by the functional role of the substituting oxide — most clearly the alkali vs. alkaline-earth distinction in the 70SiO 2 ·30R 2 O/RO series — and is the only metric in our comparison that correlates strongly with both a chemistry-based EMD and a property-prediction-based distance. It remains the metric most correlated with measured property differences, is stable under resampling of the training data, and provides a quantitative novelty scale over 4160 reference compositions, against which the isolation of a candidate glass can be ranked.