Cluster Expansion Toward Nonlinear Modeling and Classification

TL;DR

This paper introduces a non-linear cluster expansion method that leverages machine learning to accurately and efficiently model complex materials with non-linear property dependencies, overcoming limitations of traditional approaches.

Contribution

The paper presents a novel non-linear cluster expansion approach that enhances modeling accuracy for complex substitutional materials by integrating machine learning techniques.

Findings

Achieves high accuracy in modeling non-linear material properties.

Demonstrates computational efficiency over traditional methods.

Successfully applied to complex alloy systems.

Abstract

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.