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

2026/01/29 by Winfried Ripken, Michael Plainer, Gregor Lied +5 · 1 voice · 1 citation
Computer Science · #cs.LG

paper · pdf · doi:10.48550/arxiv.2601.22123

arxiv published 2026/01/29 · arxiv updated 2026/06/30

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.

Citations

• A Complete Guide to Spherical Equivariant Graph Transformers
• Improved Mean Flows: On the Challenges of Fastforward Generative Models
• AlphaFlow: Understanding and Improving MeanFlow Models
• Transferable Generative Models Bridge Femtosecond to Nanosecond Time-Step Molecular Dynamics
• ATOM: A Pretrained Neural Operator for Multitask Molecular Dynamics
• Modular MeanFlow: Towards Stable and Scalable One-Step Generative Modeling
• Learning the action for long-time-step simulations of molecular dynamics
• Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models
• Sampling 3D Molecular Conformers with Diffusion Transformers
• Align Your Flow: Scaling Continuous-Time Flow Map Distillation
• RNE: plug-and-play diffusion inference-time control and energy-based training
• FlashMD: long-stride, universal prediction of molecular dynamics
• How to build a consistency model: Learning flow maps via self-distillation
• Mean Flows for One-step Generative Modeling
• Dynamic Training Enhances Machine Learning Potentials for Long-Lasting Molecular Dynamics
• Force-Free Molecular Dynamics Through Autoregressive Equivariant Networks
• Scalable emulation of protein equilibrium ensembles with generative deep learning
• The dark side of the forces: assessing non-conservative force models for atomistic machine learning
• Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models
• On the design space between molecular mechanics and machine learning force fields
• Learning data efficient coarse-grained molecular dynamics from forces and noise
• Consistency Models Made Easy
• Transferable Boltzmann Generators
• Flow map matching with stochastic interpolants: A mathematical framework for consistency models
• Accurate structure prediction of biomolecular interactions with AlphaFold 3
• Scaling Rectified Flow Transformers for High-Resolution Image Synthesis
• Equivariant Graph Neural Operator for Modeling 3D Dynamics
• Improved Techniques for Training Consistency Models
• EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations
• Consistency Models
• Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics
• Fast Sampling of Diffusion Models via Operator Learning
• Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations
• Flow Matching for Generative Modeling
• Building Normalizing Flows with Stochastic Interpolants
• Accurate global machine learning force fields for molecules with hundreds of atoms
• SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials
• Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
• So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems
• Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics
• Learning Large-Time-Step Molecular Dynamics with Graph Neural Networks
• Geometric and Physical Quantities Improve E(3) Equivariant Message Passing
• Smooth Normalizing Flows
• Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems
• Equivariant message passing for the prediction of tensorial properties and molecular spectra
• E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
• Score-Based Generative Modeling through Stochastic Differential Equations
• Denoising Diffusion Probabilistic Models
• SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks
• Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
• Machine Learning for Molecular Simulation
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
• SchNet – A deep learning architecture for molecules and materials
• The atomic simulation environment—a Python library for working with atoms
• Attention Is All You Need
• OpenMM 7: Rapid development of high performance algorithms for molecular dynamics
• Layer Normalization
• Deep Unsupervised Learning using Nonequilibrium Thermodynamics
• Accurate sampling using Langevin dynamics
• Canonical sampling through velocity-rescaling
• Classical Mechanics
• TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials

Cited by

• Learning Structure, Energy, and Dynamics: A Survey of Artificial Intelligence for Protein Dynamics

Discussions

• Waiting for your MD simulation to finish? Visit our spotlight paper at ICML on how to train large timestep models on existing MLFF datasets in the meantime! 🗓️ Wednesday, July 8 ⏰ 10:30 AM – 12:15 PM [bsky, 2 points, 0 comments]

Related

• Learning Hamiltonian flows from numerical integrators and examples
• Learning the action for long-time-step simulations of molecular dynamics
• Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Data
• FlashMD: long-stride, universal prediction of molecular dynamics
• HMC with Normalizing Flows