# Interpretation of Crystal Energy Landscapes with Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2604.04636 · HTML: https://mlsanity.com/paper/2604.04636/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 66 references that are in the map.
- First posted on arXiv 6 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [NetScore: Towards Universal Metrics for Large-scale Performance Analysis of Deep Neural Networks for Practical On-Device Edge Usage](https://mlsanity.com/paper/1806.05512/) (2018)
- [MT-CGCNN: Integrating Crystal Graph Convolutional Neural Network with Multitask Learning for Material Property Prediction](https://mlsanity.com/paper/1811.05660/) (2018)
- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Distributed Representations of Atoms and Materials for Machine Learning](https://mlsanity.com/paper/2107.14664/) (2021)
- [Topogivity: A Machine-Learned Chemical Rule for Discovering Topological Materials](https://mlsanity.com/paper/2202.05255/) (2022)
- [Band-gap regression with architecture-optimized message-passing neural networks](https://mlsanity.com/paper/2309.06348/) (2023)
- [Material Property Prediction with Element Attribute Knowledge Graphs and Multimodal Representation Learning](https://mlsanity.com/paper/2411.08414/) (2024)
- [Predicting band gap from chemical composition: A simple learned model for a material property with atypical statistics](https://mlsanity.com/paper/2501.02932/) (2025)
- [seqKAN: Sequence processing with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2502.14681/) (2025)

## Abstract (arXiv)

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.