Robust cluster expansion of multicomponent systems using structured sparsity

Abstract

Identifying a suitable set of descriptors for modeling physical systems often utilizes either deep physical insights or statistical methods such as compressed sensing. In statistical learning, a class of methods known as structured sparsity regularization seeks to combine both physics- and statistics-based approaches. Used in bioinformatics to identify genes for the diagnosis of diseases, $\textit{group lasso}$ is a well-known example. Here in physics, we present group lasso as an efficient method for obtaining robust cluster expansions (CE) of multicomponent systems, a popular computational technique for modeling such systems and studying their thermodynamic properties. Via convex optimization, group lasso selects the most predictive set of atomic clusters as descriptors in accordance with the physical insight that if a cluster is selected, so should its subclusters. These selection rules avoid spuriously large fitting parameters by redistributing them among lower order terms, resulting in more physical, accurate, and robust CEs. We showcase these features of group lasso using the CE of bcc ternary alloy Mo-V-Nb. These results are timely given the growing interests in applying CE to increasingly complex systems, which demand a more reliable machine learning methodology to handle the larger parameter space.