Robust cluster expansion of multicomponent systems using machine learning with structured sparsity

Identifying a suitable set of descriptors for modeling physical systems often utilizes either deep physical insights or statistical methods. In machine learning, a class of methods known as structured sparsity regularization combines both physics- and statistics-based approaches. We present group lasso as an efficient method for obtaining robust cluster expansions (CE) of multicomponent systems, a popular computational technique for modeling the thermodynamic properties of such systems. 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 method to handle the larger parameter space.