Machine-learned molecular modeling of ruthenium: A Kolmogorov-Arnold Network approach

Abstract

Developing refractory high-entropy superalloys (RSAs) with performance advantages over nickel-based alloys is a critical frontier in materials science. Body-centered cubic (bcc)-based RSAs have attracted significant attention, with ruthenium (Ru) playing a key role in forming two-phase regions of A2 (disordered bcc) + B2 (ordered bcc), which could lead to superalloy-like microstructures. This study introduces the application of the Kolmogorov-Arnold Network (KAN) model to predict the mechanical and thermodynamic properties of Ru while comparing its performance against other commonly used machine-learned models. Utilizing density functional theory calculations as training data, the KAN model demonstrates superior accuracy and computational efficiency compared to conventional methods, while reducing descriptor complexity. The model accurately predicts a range of properties, including elastic constants, thermal expansion coefficients, and various moduli, with discrepancies within 6% of experimental reference data. Molecular dynamics simulations further validate the model’s efficacy, accurately capturing Ru’s phase transitions from hexagonal close-packed (hcp) to face-centered cubic structure and the melting point. This work presents the first application of KAN in materials science, demonstrating how its balanced performance and efficiency provide a new pathway for designing advanced materials, with unique advantages over conventional machine learning approaches in predicting material properties.

Keywords

Ruthenium / Kolmogorov-Arnold Network / Machine learning / Mechanical properties / Thermodynamic properties / Density-functional theory / Molecular dynamics

Acknowledgments

This work used SDSC Expanse at the San Diego Supercomputer Center through allocation BIO240093 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services and Support program supported by National Science Foundation (NSF) grants #2138259, #2138286, #2138307, #2137603, and #2138296.

Funding

J.Y. acknowledges support from the US NSF under the award CMMI-2338518.

Conflict of interest

Jingjie Yeo is an Editorial Board Member of this journal but was not in any way involved in the editorial and peer-review process conducted for this paper, directly or indirectly. Separately, other authors declared that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.

Author contributions

Conceptualization: All authors

Data curation: Zhiyu An

Formal analysis: Zhiyu An

Funding acquisition: Jingjie Yeo

Investigation: Zhiyu An

Methodology: Zhiyu An

Project administration: Jingjie Yeo

Software: Zhiyu An

Resources: Jingjie Yeo

Supervision: Jingjie Yeo

Validation: Jingjie Yeo

Visualization: Zhiyu An

Writing - original draft: Zhiyu An

Writing - review & editing: Jingjie Yeo

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Availability of data

The code and dataset for our implementation of the KAN model can be found at https://github.com/ZhiyuAn-byte/KAN-Model-for-Ru-element (doi: 10.5281/ zenodo.13856262)

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