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Cluster expansion made easy with Bayesian compressive sensing

Long-standing challenges in cluster expansion (CE) construction include choosing how to truncate the expansion and which crystal structures to use for training. Compressive sensing (CS), which is emerging as a powerful tool for model construction in physics, provides a mathematically rigorous framework for addressing these challenges. A recently-developed Bayesian implementation of CS (BCS) provides a parameterless framework, a vast speed up over current CE construction techniques, and error estimates on model coefficients. Here, we demonstrate the use of BCS to build cluster expansion models for several binary alloy systems. The speed of the method and the accuracy of the resulting fits are shown to be far superior than state-of-the-art evolutionary methods for all alloy systems shown. When combined with high throughput first-principles frameworks, the implications of BCS are that hundreds of lattice models can be automatically constructed, paving the way to high throughput thermodynamic modeling of alloys.