mlsanityData to 14 Oct 2026

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

arXiv 2601.22123 ↗First posted 29 Jan 2026cs.LGcited by 7

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Abstract (arXiv)

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.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 55 of its 95 references that are in the map. First posted on arXiv 29 Jan 2026.

Builds on

55 of 95 references.

References · 55

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38 more
  1. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
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  16. 2025Improved Mean Flows: On the Challenges of Fastforward Generative Modelscited by 110
  17. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 109
  18. 2021SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effectscited by 104
  19. 2025How to build a consistency model: Learning flow maps via self-distillationcited by 103
  20. 2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 95
  21. 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillationcited by 87
  22. 2022SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentialscited by 82
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  30. 2025Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Modelscited by 23
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50 most cited of 55 All 55 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 7.

7 papers.

  1. 2026Learning Structure, Energy, and Dynamics: A Survey of Artificial Intelligence for Protein Dynamicscited by 1
  2. 2026Generative Pseudo-Force Fields for Molecular Generationcited by 1
  3. 2026Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulationscited by 1
  4. 2026OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discoverycited by 1
  5. 2026Physics-Constrained Neural Flow Maps for Long-Horizon Prediction of Spin Dynamicscited by 0
  6. 2026Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamicscited by 0
  7. 2026Langevin Flow Maps: Efficient Molecular Dynamics and Transition Path Samplingcited by 0