{
  "abstract": "We consider a periodic scalar reaction-diffusion system over a two-dimensional domain under natural conditions on the reaction function and with initial condition $θ$. We show that on the global attractor $\\mathcal A$ of the resulting dynamical system $(u_θ(t):t>0)$, a reverse Poincaré inequality holds true, and that as a consequence the map $θ\\mapsto u_θ(t)$ satisfies an $L^2(\\Om)$-Lipschitz stability estimate on $\\mathcal A$ for any $t>0$ fixed. We then show that statistical recovery of an initial condition $θ$ in the attractor $\\mathcal A$, as well as prediction of the states $u_θ$, is possible from discrete measurements of the system at parametric $1/\\sqrt N$ convergence rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.06018",
  "author_total": 2,
  "authors": [
    {
      "name": "Dimitri Konen"
    },
    {
      "name": "Richard Nickl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90netz8jxgr85.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.06018",
  "fulltext_url": null,
  "id": "90netz8jxgr85",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.06018",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7163685918",
  "pdf_url": "https://arxiv.org/pdf/2606.06018",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90netz8jxgr85.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2606.06018",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.06018"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "On statistical inference for non-linear dynamical systems evolving in their global attractor",
  "title_text": "On statistical inference for non-linear dynamical systems evolving in their global attractor",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:40Z",
  "url": "https://research.draconitic.com/paper/90netz8jxgr85",
  "venue": "arXiv",
  "versions": []
}