Statistical Rule Learning for Materials Science

Despite notable progress in the application of machine learning to materials science, the opaque form and unsatisfactory extrapolation performance of current models precludes the discovery of novel materials or general scientific insights. Improved ML models are therefore actively researched, but their design is currently guided mainly by monitoring the average in-distribution test error. Unfortunately, this can render different models indistinguishable although their performance differs substantially across individual materials. Moreover, a sole focus on predictive performance neglects the syntactic form of the model and disregards physical knowledge that could be used to assess whether the model is likely to generalise outside of the training distribution. Here, we discuss how rule-based models can be applied to alleviate both problems. Firstly, they can be used to detect and describe the domains of applicability (DA) of complex models within a materials class. Secondly, they can directly be employed to model properties of the materials of interest. In both cases, they provide an interpretable machine learning layer to materials modelling that can drive the formulation of hypotheses and targeted acquisition of further training data.