Structure-property maps and optimal inversion in configurational thermodynamics

Cluster expansions of first-principles density-functional databases in multicomponent systems are now used as a routine tool for the prediction of zero- and finite-temperature physical properties. The ability of producing large databases of various degrees of accuracy, i.e., high-throughput calculations, makes pertinent the analysis of error propagation during the inversion process. This is a very demanding task as both data and numerical noise have to be treated on equal footing. We have addressed this problem by using an analysis that combines the variational and evolutionary approaches to cluster expansions. Simulated databases were constructed ex professo to sample the configurational space in two different and complementary ways. These databases were in turn treated with different levels of both systematic and random numerical noise. The effects of the cross-validation level, size of the database, type of numerical imprecisions on the forecasting power of the expansions were extensively analyzed. We found that the size of the database is the most important parameter. Upon this analysis, we have determined criteria for selecting the optimal expansions, i.e., transferable expansions with constant forecasting power in the configurational space (a structure-property map). As a by-product, our study provides a detailed comparison between the variational cluster expansion and the genetic-algorithm approaches.