Interpretation of Crystal Energy Landscapes with Kolmogorov-Arnold Networks

2026-04-06

AI Summary

This work addresses the limited interpretability of traditional machine learning models in predicting crystal energy landscapes, which often obscures the underlying physicochemical principles governing materials. To overcome this, the authors propose the Element-Weighted Kolmogorov–Arnold Network (EW-KAN), a novel architecture that leverages learnable activation functions and element-weighted embeddings to automatically uncover physical relationships between elemental composition and key material properties—such as formation energy, bandgap, and work function—without requiring explicit physical constraints. Evaluated on large-scale datasets, EW-KAN achieves state-of-the-art predictive accuracy while yielding learned features that align closely with periodic trends and quantum mechanical principles, thereby unifying high performance with strong interpretability.

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.

Problem

• crystal energy landscapes
• interpretability
• machine learning
• materials informatics
• scientific insight

Innovation

• Kolmogorov-Arnold Networks
• interpretable machine learning
• crystal energy landscapes
• materials informatics
• element-weighted representation