Interpretation of Crystal Energy Landscapes with Kolmogorov-Arnold Networks

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.

Figures (25)

• Figure 1: Workflow schematic of the Element-Weighted Kolmogorov–Arnold Network (EWKAN). Elemental compositions are transformed into weighted embeddings that capture each element’s contribution to the target property. These embeddings are passed into a two-layer KAN with trainable B-spline activation functions, which provide interpretable nonlinear mappings. The output layer yields property predictions such as band gap or formation energy.
• Figure 2: Bandgap prediction under EWKAN model. (a) Bandgap schematic diagram. (b) Histogram of data distribution of matbench_mp_gap. (c) MAE results for bandgap prediction under different KAN structure.
• Figure 3: Work function prediction under EWKAN model. (a) Work function schematic diagram. (b) Histogram of data distribution of JARVIS-C2DB containing work function entries. (c) MAE results for work function prediction under different KAN structure.
• Figure 4: Formation energy prediction under EWKAN model. (a) Formation energy schematic diagram(take sodium chloride as an example). (b) Histogram of data distribution of JARVIS-DFT containing formation energy entries. (c) MAE results for formation energy prediction under different KAN structure.
• Figure 5: Comparison of (a) the original PC1 values obtained from the KAN model and (b) normalized Pauling electronegativity across the periodic table layout. The close resemblance between the two maps indicates that the dominant latent axis learned by the model captures an effective “electronegativity–metallicity” dimension, highlighting the emergence of chemically interpretable features from a purely data-driven representation. According to the PCA variance analysis (Fig. \ref{['fig:pca_var']}), the PC1 achieves 32.69% variance while the first four components account for over 80% of the total variance