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

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.