{
  "abstract": "Chaotic systems often evolve on a low-dimensional attractor whose geometry varies from one region to another. We propose a non-intrusive reduced-order model that reads this local geometry by clustering and uses it to shape a radial basis library whose kernels adapt to each region. Fitting the reduced velocity onto this library by one global least-squares solve gives an explicit, differentiable vector field that reproduces the long-term statistics without any use of the governing equations. A radial basis field decays away from the data and cannot by itself return an escaped state. The integration is therefore stabilised by a kinematic corrector, whose reported magnitude measures how far each result rests on the learned field. On Lorenz-63 the model recovers the attractor, its marginal densities and its Lyapunov spectrum. On Lorenz-96 its valid prediction time matches typical configurations of neural-network and reservoir-computing forecasters and trails their best-tuned ones, and the invariant measure is reproduced on both the full state and on a reduced observable. On the Kuramoto--Sivashinsky equation and the quasiperiodic Kolmogorov flow the model matches the energy distribution and spectrum of an intrusive quantised-local Galerkin model and improves on a global Galerkin projection of the same reduced dimension. The recovery is dictated by the distance from a state to its nearest kernels, not by the one-step regression error.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.08571",
  "author_total": 3,
  "authors": [
    {
      "name": "Miguel Pérez Cuadrado"
    },
    {
      "name": "Giorgio Maria Cavallazzi"
    },
    {
      "name": "Alfredo Pinelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8sp2nmdm73qjc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.08571",
  "fulltext_url": null,
  "id": "8sp2nmdm73qjc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.08571",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7167896168",
  "pdf_url": "https://arxiv.org/pdf/2607.08571",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8sp2nmdm73qjc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2607.08571",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.08571"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Manifold-adapted radial basis functions for reduced-order modelling of chaotic flows",
  "title_text": "Manifold-adapted radial basis functions for reduced-order modelling of chaotic flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/8sp2nmdm73qjc",
  "venue": "arXiv",
  "versions": []
}