  Glass hardness varies in a non-linear fashion with the chemical composition
and applied load, a phenomenon known as the indentation size effect (ISE),
which is challenging to predict quantitatively. Here, using a curated dataset
of over approx. 3000 inorganic glasses from the literature comprising the
composition, 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 the
training, the standard data-driven ML model failed to capture the ISE. To
address this gap, we combined an empirical expression (Bernhardt law) to
describe the ISE with ML to develop a framework that incorporates the symbolic
law representing the domain reasoning in ML, namely Symbolic Reasoning-Informed
ML Procedure (SRIMP). We show that the resulting SRIMP outperforms the
data-driven ML model in predicting the ISE. Finally, we interpret the SRIMP
model to understand the contribution of the glass network formers and modifiers
toward composition and load-dependent (ISE) and load-independent hardness. The
deconvolution of the hardness into load-dependent and load-independent terms
paves the way toward a holistic understanding of composition and ISE in
glasses, enabling the accelerated discovery of new glass compositions with
targeted hardness.
