Kolmogorov-Arnold Networks Applied to Materials Property Prediction

TL;DR

This paper explores Kolmogorov-Arnold Networks (KANs) as an alternative to traditional neural networks for predicting materials properties, highlighting their interpretability and parameter efficiency, with comparative analysis against random forests.

Contribution

The study demonstrates the application of KANs to materials property prediction, showing they can achieve comparable accuracy to established models with simpler, more interpretable forms.

Findings

KANs are competitive with random forests in 5% of cases.

Tuning KAN architectures reduces errors by 10-20%.

Simple KAN models produce predictions similar to complex deep neural networks.

Abstract

Kolmogorov-Arnold Networks (KANs) were proposed as an alternative to traditional neural network architectures based on multilayer perceptrons (MLP-NNs). The potential advantages of KANs over MLP-NNs, including significantly enhanced parameter efficiency and increased interpretability, make them a promising new regression model in supervised machine learning problems. We apply KANs to prediction of materials properties, focusing on a diverse set of 33 properties consisting of both experimental and calculated data. We compare the KAN results to random forest, a method that generally gives excellent performance on a wide range of properties predictions with very little optimization. The KANs were worse, on par, or better than random forest about 35%, 60%, and 5% of the time, respectively, and KANs are in practice more difficult to fit than random forest. By tuning the network architecture, we found property fits often resulted in 10-20% lower errors compared to the standard KAN, and typically gave results comparable to random forest. In the specific context of predicting reactor pressure vessel transition temperature shifts, we explored the parameter efficiency and the interpretable power of KANs by comparing predictions of simple KAN models (e.g., < 50 parameters) and closed-form expressions suggested by the KAN fits to previously published deep MLP-NNs and hand-tuned models created using domain expertise of embrittlement physics. We found that simple KAN models and the resulting closed-form expressions produce prediction errors on par with established hand-tuned models with a comparable number of parameters, and required essentially no domain expertise to produce. These findings reinforce the potential applicability of KANs for machine learning in materials science and suggest that KANs should be explored as a regression model for prediction of materials properties.