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

TL;DR

This paper presents a novel machine learning framework for learning Hamiltonian flow maps that enable stable, large-timestep simulations of Hamiltonian systems, overcoming traditional numerical stability constraints.

Contribution

It introduces a mean flow consistency condition for training on independent samples, allowing large-timestep updates without trajectory data, and improves molecular dynamics simulations with ML force fields.

Findings

Supports significantly larger timesteps in simulations

Maintains comparable training and inference costs

Validated across diverse Hamiltonian systems

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.