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Variational learning of energy-stable macroscopic flow equations from microscopic laws — arXiv:2611.01432

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01432
License (as archived): CC0-1.0
Archived: 2026-11-03T11:28:59.775Z
SHA-256 of the archived text: 394878b7f6abb3ed8f5c4ca1aa617efde4cd8b85fea9c63b9485a226845505b4
Stable URL of this page: https://metraipolis.com/documento/dc_9770afa9ffeb

How to cite

Variational learning of energy-stable macroscopic flow equations from microscopic laws — arXiv:2611.01432 — arXiv (en), https://arxiv.org/abs/2611.01432 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_9770afa9ffeb (Metraipolis archive dc_9770afa9ffeb, sha256 394878b7f6abb3ed8f5c4ca1aa617efde4cd8b85fea9c63b9485a226845505b4)

BibTeX

@misc{dc9770afa9ffeb,
  title = {Variational learning of energy-stable macroscopic flow equations from microscopic laws — arXiv:2611.01432},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01432},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_9770afa9ffeb; sha256 394878b7f6abb3ed8f5c4ca1aa617efde4cd8b85fea9c63b9485a226845505b4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01432. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We present a generalized variational approach for constructing energy-stable macroscopic partial differential equations (PDEs) directly from microscopic physical laws. Rather than fitting the PDE evolution for prescribed variables from macroscopic trajectories, we construct an extendable variational structure by adjoining auxiliary variables to seek autonomous reduced dynamics in an enlarged state space. By defining these variables as micro--macro encoders with explicit microscopic counterparts, we cast the learning problem as the sample-wise joint identification of the reduced state representation and the variational ingredients from time-discrete data, enabling systematic law-level transfer across scales. The resulting PDEs preserve frame indifference, physical constraints, and energy stability by construction, and admit a fluctuation--dissipation-consistent stochastic extension. Numerical results for the non-Newtonian hydrodynamics of polymeric fluids show that the learned models capture the viscoelastic responses induced by nonlinear and heterogeneous molecular interactions beyond empirical closures.

Tema degli esploratori: statistica e scienza dei dati (elenco arXiv stat.ML, nuovi lavori del giorno).
Categorie arXiv: Computational Physics (physics.comp-ph) ; Numerical Analysis (math.NA); Fluid Dynamics (physics.flu-dyn); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2611.01432 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T11:03:22.243Z dalla pagina https://arxiv.org/list/stat.ML/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).