Interpretation of Crystal Energy Landscapes with Kolmogorov-Arnold Networks

TL;DR

This paper introduces Kolmogorov-Arnold Networks (KANs), an interpretable machine learning framework that predicts crystal properties accurately while revealing underlying chemical and physical principles.

Contribution

The development of KANs, which combine high predictive accuracy with interpretability, bridging machine learning and physical chemistry in materials science.

Findings

KANs achieve state-of-the-art accuracy in property prediction.

KANs uncover interpretable chemical trends aligned with the periodic table.

Embedding analysis reveals physical relationships without explicit constraints.

Abstract

Characterizing crystalline energy landscapes is essential to predicting thermodynamic stability, electronic structure, and functional behavior. While machine learning (ML) enables rapid property predictions, the "black-box" nature of most models limits their utility for generating new scientific insights. Here, we introduce Kolmogorov-Arnold Networks (KANs) as an interpretable framework to bridge this gap. Unlike conventional neural networks with fixed activation functions, KANs employ learnable functions that reveal underlying physical relationships. We developed the Element-Weighted KAN, a composition-only model that achieves state-of-the-art accuracy in predicting formation energy, band gap, and work function across large-scale datasets. Crucially, without any explicit physical constraints, KANs uncover interpretable chemical trends aligned with the periodic table and quantum mechanical principles through embedding analysis, correlation studies, and principal component analysis. These results demonstrate that KANs provide a powerful framework with high predictive performance and scientific interpretability, establishing a new paradigm for transparent, chemistry-based materials informatics.