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.
@article{arxiv.2601.22123,
title = {Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics},
author = {Winfried Ripken and Michael Plainer and Gregor Lied and Thorben Frank and Oliver T. Unke and Stefan Chmiela and Frank Noé and Klaus-Robert Müller},
journal= {arXiv preprint arXiv:2601.22123},
year = {2026}
}