Bridging Molecular Scales with Implicit Score Matching for Bottom-Up Coarse Graining

Abstract

Molecular dynamics simulations provide a computational microscope for atomic scale processes but remain restricted to relatively small spatial and temporal scales. Coarse-grained models extend their reach by representing groups of atoms as effective interaction sites. The number of particles is systematically reduced by embedding the collective behavior of groups of atoms into coarse-grained sites governed by effective potentials. However, constructing accurate, highly coarsened potentials, even with the assistance of modern machine-learning methods, is a grand challenge because coarse grained forces depend on a statistical distribution of composite atomic configurations making direct calculation computationally prohibitive. Here, we introduce an alternative framework based on implicit score matching that directly avoids the need for explicit coarse-grained forces. This approach both substantially reduces the training data required relative to conventional force-matching methods and enables high-fidelity models in which each coarse-grained site represents hundreds to thousands of atoms. We demonstrate the method's versatility and effectiveness across a diverse range of chemical systems and phenomena, developing bottom-up, machine-learned models. These enable efficient modeling at micrometer and millimeter length scales, while retaining significant amounts of the atomic scale fidelity. These results establish implicit score matching as a practical route towards chemically accurate simulations that bridge molecular and mesoscopic scales.