{
  "abstract": "We develop a rigorous justification for a parameter estimation algorithm which couples continuous data assimilation to generic optimization. For finite dimensional systems, we provide a rigorous justification of an asymptotic approximation of the sensitivity for the underlying modeled dynamical system, prove that the $L^2$ loss function satisfies an approximate Polyak-Lojasiewicz inequality, and use that result to justify convergence of gradient descent for the proposed algorithm. Numerical examples are provided that demonstrate the precision of the rigorous results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02686",
  "author_total": 2,
  "authors": [
    {
      "name": "Joshua Newey"
    },
    {
      "name": "Jared P. Whitehead"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9jq5qqj7t6xwt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02686",
  "fulltext_url": null,
  "id": "9jq5qqj7t6xwt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02686",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.02686",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9jq5qqj7t6xwt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.02686",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02686"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Asymptotic approximation of sensitivities in finite dimensional continuous data assimilation with application to parameter estimation",
  "title_text": "Asymptotic approximation of sensitivities in finite dimensional continuous data assimilation with application to parameter estimation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/9jq5qqj7t6xwt",
  "venue": "arXiv",
  "versions": []
}