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Ab initio prediction of the variation of properties in the configurationalspace of solid solutions is computationally very demanding. We present anapproach to accelerate these predictions via a combination of densityfunctional theory and machine learning, using the cubic spinel nitrideGeSn$_2$N$_4$ as a case study, exploring how formation energy and electronicbandgap are affected by configurational variations. Furthermore, we demonstratethe utility of applying explainable machine learning to understand the crystalchemistry origins of the trends that we observe. Different configurationdescriptors (Coulomb matrix eigenspectrum, many-body tensor representation, andcluster correlation function vectors) are combined with different models(linear regression, gradient-boosted decision tree, and multi-layer perceptron)to extrapolate the calculation of ab initio properties from a small set ofconfigurations to the full space with thousands of configurations. We discussthe performance of different descriptors and models. SHAP (SHapley AdditiveexPlanations) analysis of the machine learning models highlights how values offormation energy are dominated by variations in local crystal structure (singlepolyhedral environments), while values of electronic bandgap are dominated byvariations in more extended structural motifs. Finally, we demonstrate theusefulness of this approach by constructing structure-property maps,identifying important configurations of GeSn$_2$N$_4$ with extremal properties,as well as by calculating accurate equilibrium properties using configurationalaveraging.

Spinel nitride solid solutions: charting properties in the configurational space with explainable machine learning