Entanglement-aware Flow Matching for Polymer Dynamics

Learning long-timescale dynamics in dense polymer systems is important for understanding material behavior, but remains difficult because chain motion is governed by entanglement, a collective topological constraint that existing learned dynamics models often fail to preserve during generation. We formulate windowed Conditional Flow Matching (wCFM) for force-free polymer dynamics, training continuous-time velocity fields on trajectory windows sampled across multiple temporal scales. We further introduce orthF, a geometry-aware regularization that penalizes predicted motion across local inter-chain boundaries. We evaluate orthF on molecular dynamics trajectories of dense polymer systems across three dynamics models, showing that its benefit is not limited to a single architecture. Across 9 polymer datasets,orthF improves aggregate displacement accuracy for all three models, yielding generated trajectories that better match ground-truth distributions and structural and topology-related observables. Once trained, our approach generates a 50ns backbone trajectory in 13s on a single GPU, compared with 43h for all-atom molecular dynamics on 64 CPUs, corresponding to an approx 1.2x 10^4 wall-clock sampling-time ratio. These results show that explicit geometric inductive bias is a simple and effective way to improve learned dynamics in entangled molecular systems.