Metraipolis › archive › dc_fe36364398be

Solving and Learning Navier-Stokes Dynamics with the Neural Basis Method — arXiv:2610.32167

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.32167
License (as archived): CC0-1.0
Archived: 2026-10-26T20:14:10.030Z
SHA-256 of the archived text: 65f38a48abfef156afed57e226744e93af5cf5cc2b55c453de81fae28372b722
Stable URL of this page: https://metraipolis.com/documento/dc_fe36364398be

How to cite

Solving and Learning Navier-Stokes Dynamics with the Neural Basis Method — arXiv:2610.32167 — arXiv (en), https://arxiv.org/abs/2610.32167 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fe36364398be (Metraipolis archive dc_fe36364398be, sha256 65f38a48abfef156afed57e226744e93af5cf5cc2b55c453de81fae28372b722)

BibTeX

@misc{dcfe36364398be,
  title = {Solving and Learning Navier-Stokes Dynamics with the Neural Basis Method — arXiv:2610.32167},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.32167},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fe36364398be; sha256 65f38a48abfef156afed57e226744e93af5cf5cc2b55c453de81fae28372b722},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.32167. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Physics-informed machine learning has become a major direction in predictive modeling of fluid dynamics, combining governing physics with learned representations. Yet prevailing formulations neither guarantee that small PDE-residual losses imply small solution errors nor scale effectively with increasing problem size. Here we present the neural basis method (NBM) as a new approach for Navier--Stokes dynamics. NBM is built on a ``representation-then-projection'' principle: fixed neural bases define the representation space, while projection of the governing equations determines the expansion coefficients. The same bases define common coordinates for the parametric solution manifold, recasting operator learning as a parameter-to-coefficient mapping and enabling scalability by removing explicit spatial dependence. For incompressible flow, NBM yields a velocity-only formulation whose residual provides an a posteriori velocity-error estimate, establishing a certified, data-free training objective for coefficient learning. Theoretical analysis and numerical experiments demonstrate the accuracy, efficiency, generalization, and scalability of NBM, with substantial improvements over baselines.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Fluid Dynamics (physics.flu-dyn) ; Machine Learning (cs.LG); Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2610.32167 — 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 2026-10-26T19:49:03.467Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).