Interfacial topological selection links structural motifs to the free-energy barrier in methane hydrate nucleation.

HYPOTHESIS: Methane hydrate nucleation is a stochastic process critical to energy and flow-assurance technologies, yet the structural changes associated with crossing its free-energy barrier remain poorly resolved. We hypothesize that transient topological motifs in the interface hydrogen-bonded network provide information about barrier crossing beyond bulk nucleus growth alone. SIMULATIONS: To test this hypothesis, we integrate molecular dynamics (MD) simulations with machine learning (ML). We perform 20 independent, long-timescale MD simulations of methane hydrate nucleation and identify transient structural motifs using the Hierarchical Topological Ring algorithm, including polyhedral cages and ternary water-ring aggregations (TWRAs). Time-lagged independent component analysis (tICA) is applied to construct a free-energy landscape, while extreme gradient boosting (XGBoost) with Local Interpretable Model-Agnostic Explanations (LIME) interpretation quantifies associations between structural descriptors and the resulting free-energy coordinate. Trajectory-level data partitioning is used for model evaluation. FINDINGS: Across the nucleation trajectories, barrier ascent is accompanied by depletion of topologically incompatible 2-1-0 TWRAs and enrichment of compatible 0-3-0 and 0-2-1 motifs at the hydrate-water interface. The XGBoost/LIME analysis identifies these TWRA proportions as informative structural descriptors of free-energy coordinate. In trajectory-level leave-one-out cross-validation, adding the three key TWRA proportions to the instantaneous free energy improves prediction of subsequent free-energy evolution at 50-100 ns relative to using instantaneous free energy alone. These results support interfacial topological selection as a structural signature of barrier crossing and connect local hydrogen-bonded network reorganization with the free-energy evolution of methane hydrate nucleation.