Local Variational Graph Coarsening for Machine Learning Coarse-Grained Molecular Dynamics Simulations

Coarse-grained (CG) molecular dynamics (MD) simulations can simulate large molecular complexes over extended time scales by reducing degrees of freedom. A central challenge in CG modeling is the selection of the CG mapping algorithm, which directly influences both accuracy and the interpretability of the model. Despite significant progress, effective strategies for optimal CG mappings remain a challenging task, highlighting the necessity for a comprehensive computational framework. In this work, we introduce a multilevel graph-coarsening framework for coarse graining, inspired by recent advances in graph reduction with spectral and cut guarantees. CG sites are generated through edge contractions based on a local variational cost metric, while preserving essential spectral properties of the original graph. This construction ensures structural fidelity across scales. To learn the corresponding CG energy functions, we utilize the Message Passing Atomic Cluster Expansion (MACE), yielding efficient yet accurate CG potentials. We demonstrate the generality of the framework across isolated molecules, bulk molecular liquid, and crystal. Our approach provides a data-driven bottom-up computational framework for the development of systematically improvable CG potentials with controlled accuracy and physical interpretability.