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Glass hardness varies in a non-linear fashion with the chemical compositionand applied load, a phenomenon known as the indentation size effect (ISE),which is challenging to predict quantitatively. Here, using a curated datasetof over approx. 3000 inorganic glasses from the literature comprising thecomposition, indentation load, and hardness, we develop machine learning (ML)models to predict the composition and load dependence of Vickers hardness.Interestingly, when tested on new glass compositions unseen during thetraining, the standard data-driven ML model failed to capture the ISE. Toaddress this gap, we combined an empirical expression (Bernhardt law) todescribe the ISE with ML to develop a framework that incorporates the symboliclaw representing the domain reasoning in ML, namely Symbolic Reasoning-InformedML Procedure (SRIMP). We show that the resulting SRIMP outperforms thedata-driven ML model in predicting the ISE. Finally, we interpret the SRIMPmodel to understand the contribution of the glass network formers and modifierstoward composition and load-dependent (ISE) and load-independent hardness. Thedeconvolution of the hardness into load-dependent and load-independent termspaves the way toward a holistic understanding of composition and ISE inglasses, enabling the accelerated discovery of new glass compositions withtargeted hardness.

Glass Hardness: Predicting Composition and Load Effects via Symbolic Reasoning-Informed Machine Learning