Graph-Coarsening for Machine Learning Coarse-grained Molecular Dynamics

Coarse-grained (CG) molecular dynamics (MD) simulations can simulate large molecular complexes over extended timescales by reducing degrees of freedom. A critical step in CG modeling is the selection of the CG mapping algorithm, which directly influences both accuracy and interpretability of the model. Despite progress, the optimal strategy for coarse-graining remains a challenging task, highlighting the necessity for a comprehensive theoretical framework. In this work, we present a graph-based coarsening approach to develop CG models. Coarse-grained sites are obtained through edge contractions, where nodes are merged based on a local variational cost metric while preserving key spectral properties of the original graph. Furthermore, we illustrate how Message Passing Atomic Cluster Expansion (MACE) can be applied to generate ML-CG potentials that are not only highly efficient but also accurate. Our approach provides a bottom-up, theoretically grounded computational method for the development of systematically improvable CG potentials.