Cluster expansion toward nonlinear modeling and classification

A quantitative first-principles description of complex substitutional materials such as alloys is challenging due to the vast number of configurations and the high computational cost of solving the quantum mechanical problem. Therefore, materials properties must be modeled. The cluster expansion (CE) method is widely used for this purpose, but it struggles with properties that exhibit nonlinear dependencies on composition, often failing even in a qualitative description. By looking at CE through the lens of machine learning, we resolve this severe problem and introduce a nonlinear CE approach, yielding extremely accurate and computationally efficient results as demonstrated by distinct examples.