Realistic physical systems are characterised by emergent interactions across multiple length and time scales, posing a significant challenge for predictive machine learning (ML) models. Most scientific ML models focus on a narrow range of interactions. While machine learning force fields (MLFFs) offer near-quantum accuracy, the ubiquitous message-passing layers miss long-range many-body effects. Here we introduce the Multiscale Structural Ensemble (MuSE), a hierarchical model that uses Soft Coarse-Graining Pooling to construct coarse representations from smooth fractional assignments of atoms to coarse nodes, enabling MLFF modules to operate across multiple scales. MuSE is architecture-agnostic and coupled with SO3krates, MACE, and PaiNN MLFFs for both molecules and materials. We demonstrate the power of MuSE through Hessian-based benchmarks, folding trajectories for biomolecules, and energy profiles in molecule-graphene nanostructures, where MuSE accurately captures quantum-mechanical interactions at relevant scales -- unlike other recent long-range ML models.
@article{arxiv.2605.25710,
title = {Machine Learning Multiscale Interactions},
author = {Àlex Solé and Sergio Suárez-Dou and Albert Mosella-Montoro and Silvia Gómez-Coca and Eliseo Ruiz and Alexandre Tkatchenko and Javier Ruiz-Hidalgo},
journal= {arXiv preprint arXiv:2605.25710},
year = {2026}
}