{
  "abstract": "Many approaches have recently been proposed to combine data assimilation with machine learning for improved forecasts with geophysical models. Here, we focus on combining advanced sequential data assimilation schemes with a generative forecasting model which accounts for complex model errors. This generative model provides a stochastic approximation of the conditional distribution of the successor state given the current state. The proposed variational formulation is a novel one-step weak-constraint 4D-Var scheme in which a learned conditional stochastic forecast replaces the prescribed additive Gaussian model error representation. We derive and implement this formulation as an ensemble variational algorithm, the generative iterative ensemble Kalman filter (IEnKF-G), which generalises the iterative ensemble Kalman filter with additive Gaussian model error (IEnKF-Q). We extend the method to a smoother with an assimilation window spanning multiple time steps and propose a simplified variant. The IEnKF-G is evaluated on a stochastic variant of the Lorenz 1963 model to assess its robustness. It is then tested on a multi-scale variant of the one-dimensional Lorenz 1996 model, in which the resolved variables are affected by model error originating from the hidden small-scale variables. The algorithm is then compared to an ensemble Kalman filter that adaptively mitigates model and sampling errors, and to the IEnKF-Q. The IEnKF-G is generally more accurate in the tested configurations, with substantial gains under partial observations and significant model error. This demonstrates the potential of generative data-driven models when paired with classical data assimilation methods, particularly when model error is substantial.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17333",
  "author_total": 3,
  "authors": [
    {
      "name": "Marc Bocquet"
    },
    {
      "name": "Tobias S. Finn"
    },
    {
      "name": "Sibo Cheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a0p8xy5zf0ab7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17333",
  "fulltext_url": null,
  "id": "a0p8xy5zf0ab7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17333",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.ao-ph"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1902|Meteorological Phenomena and Simulations"
    ]
  ],
  "openalex": "W7221780253",
  "pdf_url": "https://arxiv.org/pdf/2610.17333",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a0p8xy5zf0ab7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.17333",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17333"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.ao-ph",
      "subfield": "atmospheric"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Accounting for model error in ensemble variational data assimilation through learned generative dynamics",
  "title_text": "Accounting for model error in ensemble variational data assimilation through learned generative dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/a0p8xy5zf0ab7",
  "venue": "arXiv",
  "versions": []
}