Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics
This work addresses a bottleneck in molecular dynamics simulations for researchers, enabling more efficient long-time evolution predictions with larger timesteps, though it appears incremental as it builds on prior machine-learned force field approaches.
The paper tackles the problem of simulating long-time evolution in Hamiltonian systems, which is limited by small timesteps for stability, by introducing a framework to learn Hamiltonian Flow Maps that predict mean phase-space evolution, enabling stable large-timestep updates beyond classical integrators. The method improves molecular dynamics simulations with machine-learned force fields, supporting significantly larger integration timesteps while trained on trajectory-free datasets.
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.