Cluster Expansion Toward Nonlinear Modeling and Classification

A quantitative first-principles description of complex substitutional materials like 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 non-linear 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 non-linear CE approach, yielding extremely accurate and computationally efficient results as demonstrated by distinct examples.