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

Winfried Ripken, Michael Plainer, Gregor Lied, Thorben Frank, Oliver T. Unke, Stefan Chmiela, Frank Noe, Klaus Robert Muller

Keywords: Hamiltonian Mechanics, Molecular Dynamics, Integration, Flow Maps, Mean Flow

TL;DR: We introduce a trajectory-free, consistency-based training objective to learn Hamiltonian flow maps from instantaneous supervision, enabling large-timestep molecular dynamics from standard MLFF datasets.

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 $\Delta t$, 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.

Submission Track: Full Paper

Submission Category: AI-Guided Design

Submission Number: 13