Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics

• URL: http://arxiv.org/abs/2601.22123v2
• Date: Fri, 30 Jan 2026 11:02:04 GMT
• Title: Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics
• Abstract summary: We introduce a framework to learn Hamiltonian Flow Maps by predicting the mean phase-space evolution over a chosen time span.<n>Our method in particular improves upon molecular dynamics simulations using machine-learned force fields.
• Score: 16.337945610431785
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the mean phase-space evolution over a chosen time span, enabling stable large-timestep updates far beyond the stability limits of classical integrators. To this end, we impose a Mean Flow consistency condition for time-averaged Hamiltonian dynamics. Unlike prior approaches, this allows training on independent phase-space samples without access to future states, avoiding expensive trajectory generation. Validated across diverse Hamiltonian systems, our method in particular improves upon molecular dynamics simulations using machine-learned force fields (MLFF). Our models maintain comparable training and inference cost, but support significantly larger integration timesteps while trained directly on widely-available trajectory-free MLFF datasets.

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