{
  "abstract": "A foundational principle in nonlinear dynamics is that the structure of a dynamical system can be recovered from a small number of generic measurements or coordinates. We develop an analogous principle for the identification of dynamic models for time series \\textit{with noise}, which builds on previous identification results for noiseless dynamical systems. The noise is allowed to be non-iid, non-Gaussian, and dependent on the state. Our results cover noisily observed differential equations and discrete-time dynamical systems, as well as stochastic models with process noise. We illustrate the utility of this identification principle using a Lorenz-63 model and a Hénon map model, both with observational noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.16035",
  "author_total": 2,
  "authors": [
    {
      "name": "Michael Wieck-Sosa"
    },
    {
      "name": "Cosma Rohilla Shalizi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4m9bqye6etm2w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.16035",
  "fulltext_url": null,
  "id": "4m9bqye6etm2w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.16035",
  "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",
      "math.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "arxiv",
      "physics.data-an"
    ],
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      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2207|Control Systems and Identification"
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  ],
  "openalex": "W7169923874",
  "pdf_url": "https://arxiv.org/pdf/2607.16035",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4m9bqye6etm2w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2607.16035",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.16035"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Dynamic models with $p$ parameters are identified by $2p+1$ random features",
  "title_text": "Dynamic models with p parameters are identified by 2p+1 random features",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/4m9bqye6etm2w",
  "venue": "arXiv",
  "versions": []
}