{
  "abstract": "Reconstructing turbulent flow fields from sparse and irregular measurements remains challenging because the underlying inverse problem is severely underdetermined. Here we present MANTRA, a manifold-based tensor framework that represents each velocity component in a continuous tensor-product space while constraining its coefficient tensor to a low-rank Tucker manifold. This structure provides a compact, data-adaptive representation without requiring gridded observations or governing equations. Riemannian optimization and adaptive selection of rank and basis complexity enable the model to exploit coordinate-wise spatiotemporal correlations. In simulations of forced isotropic turbulence and flow over a cylinder, MANTRA recovers multiscale structures at sampling densities orders of magnitude below the underlying grids and remains accurate under Gaussian noise up to 20% of the peak velocity. It also recovers leading coordinate-wise correlation structures from sparse observations. Applied to experimental particle-tracking velocimetry of an oscillating impinging jet, MANTRA reveals time-evolving structures that are not apparent from the scattered measurements alone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08411",
  "author_total": 3,
  "authors": [
    {
      "name": "Nazmus Sakib"
    },
    {
      "name": "Alexander G. Mychkovsky"
    },
    {
      "name": "Hessam Babaee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2g21f6m2adzqj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08411",
  "fulltext_url": null,
  "id": "2g21f6m2adzqj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08411",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.flu-dyn"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08411",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2g21f6m2adzqj.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.08411",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08411"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Low-Rank Tensor Manifolds for Turbulent Field Reconstruction from Sparse Data",
  "title_text": "Low-Rank Tensor Manifolds for Turbulent Field Reconstruction from Sparse Data",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:41Z",
  "url": "https://research.draconitic.com/paper/2g21f6m2adzqj",
  "venue": "arXiv",
  "versions": []
}