Thermo-Symplectic Neural Langevin Flows

Molecular dynamics (MD) underlies biomolecular simulation by modeling atomistic motion over physical time. In thermostatted settings, this evolution is formulated as underdamped Langevin dynamics on position-momentum phase space, whose sequential force-driven integration makes long-horizon simulation computationally expensive. Recent learning-based approaches aim to reduce this cost by modeling molecular trajectories or state evolution from simulation data, but they overlook its underlying geometry. In this work, we formulate molecular dynamics as a learnable Lie--Stratonovich stochastic flow on phase space. We further embed the intrinsic thermo-symplectic structure of underdamped Langevin dynamics into the learned stochastic flow. On realistic solvated protein systems from \textsf{mdCATH}, our method outperforms existing baselines in trajectory reconstruction and conformal-symplectic preservation, while maintaining low computational cost. These results demonstrate that preserving the geometric structure of Langevin dynamics provides an effective inductive bias for accurate and physically consistent modeling of molecular dynamics.