Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics
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arXiv
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| Autori principali: | , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866915819658674176 |
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| author | Ripken, Winfried Plainer, Michael Lied, Gregor Frank, Thorben Unke, Oliver T. Chmiela, Stefan Noé, Frank Müller, Klaus-Robert |
| author_facet | Ripken, Winfried Plainer, Michael Lied, Gregor Frank, Thorben Unke, Oliver T. Chmiela, Stefan Noé, Frank Müller, Klaus-Robert |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22123 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics Ripken, Winfried Plainer, Michael Lied, Gregor Frank, Thorben Unke, Oliver T. Chmiela, Stefan Noé, Frank Müller, Klaus-Robert Machine Learning 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. |
| title | Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.22123 |