A multi-scale mixture of experts model for cross-size structural prediction of Cu nanoparticles

Zhang, Yunyu, Butler, Keith T. and Catlow, C. Richard A. ORCID: https://orcid.org/0000-0002-1341-1541 2026. A multi-scale mixture of experts model for cross-size structural prediction of Cu nanoparticles. npj Computational Materials 10.1038/s41524-026-02280-x

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Abstract

Predicting structures and energetics of metallic nanoparticles across wide size ranges remains challenging because the balance of interaction scales changes rapidly with system size. We introduce a multi-scale Mixture-of-Experts (MoE) architecture for Cu clusters and nanoparticles that explicitly separates short-, medium-, and long-range interactions using three specialised machine-learning interatomic potential experts combined through a learnable size-conditioned gating network. The resulting MoE aggregates per-atom energies into a single conservative potential, ensuring forces are obtained as energy gradients and enabling stable molecular dynamics. Across mixed cluster-nanoparticle test sets, the MoE improves accuracy relative to both an off-the-shelf foundation potential and a finetuned single-expert baseline. Stress tests show that force errors remain comparatively stable across cluster sizes and that the model retains robust energetics under morphology out-of-distribution shifts quantified using a structural outlier score based on similarity measures. The learned gating weights further provide an interpretable, size-dependent decomposition of interaction scales. Finally, validation against linear-scaling density functional theory using the ONETEP code, together with finite-temperature molecular dynamics tests, demonstrates consistent energetics, stable force behaviour, and well-behaved dynamical trajectories, supporting the use of the model for efficient structural optimisation and configurational sampling across nanoparticle sizes.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Physical, Chemical & Environmental Sciences
Publisher:	Nature Research
ISSN:	2057-3960
Date of First Compliant Deposit:	1 September 2026
Date of Acceptance:	4 August 2026
Last Modified:	01 Sep 2026 12:00
URI:	https://orca.cardiff.ac.uk/id/eprint/189300

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