{
  "abstract": "This paper introduces an online evolve--filter--relax (EFR) strategy for long-term stability of Operator Inference (OpInf) reduced-order models (ROMs) of complex fluid flow simulations. The main novelty of the new EFR-OpInf strategy is the use of online (i.e., at the learned ROM online evaluation level) spatial filtering inspired from large eddy simulation to significantly improve long-term stability and predictive performance of standard OpInf. Furthermore, the EFR-OpInf strategy reduces, and in some cases even eliminates, the need for standard $L^2$ regularization, while providing physical interpretability for the OpInf hyperparameters. The EFR-OpInf framework is modular, readily integrated into existing OpInf workflows, and accommodates a user-selected ROM filtering strategy. We demonstrate the EFR-OpInf's effectiveness using a fully non-intrusive projection-based ROM filter, a ROM differential filter, and a hybrid projection-differential ROM filter. The new EFR-OpInf models are evaluated on a high-Péclet-number convection--diffusion--reaction problem that embeds the variation in one parameter and two unsteady Navier--Stokes problems that focus on predictions beyond a training horizon: a transitional two-dimensional flow past a cylinder and a three-dimensional turbulent minimal channel flow. Across these three scenarios, EFR-OpInf can reduce prediction errors by up to an order of magnitude relative to standard OpInf. Moreover, EFR-OpInf remains stable over long prediction horizons in cases where standard OpInf diverges. Depending on the ROM filter used, EFR-OpInf's computational cost is comparable to that of standard OpInf.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14812",
  "author_total": 7,
  "authors": [
    {
      "name": "Ian Moore"
    },
    {
      "name": "Ping-Hsuan Tsai"
    },
    {
      "name": "Anthony Gruber"
    },
    {
      "name": "Ionuţ Farcaş"
    },
    {
      "name": "Christopher Wentland"
    },
    {
      "name": "Irina Tezaur"
    },
    {
      "name": "Traian Iliescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7kmdqnn77hsm7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14812",
  "fulltext_url": null,
  "id": "7kmdqnn77hsm7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14812",
  "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.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.14812",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7kmdqnn77hsm7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14812",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14812"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Learning Long-Term Stable Operator Inference Reduced-Order Models of Fluid Flows through Online Spatial Filtering",
  "title_text": "Learning Long-Term Stable Operator Inference Reduced-Order Models of Fluid Flows through Online Spatial Filtering",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7kmdqnn77hsm7",
  "venue": "arXiv",
  "versions": []
}