{
  "abstract": "We develop a hybrid modeling framework for coupling pre-trained numerics-informed neural networks (NINNs) with classical full order models (FOMs) using the overlapping Schwarz alternating method. We consider the two-dimensional advection-diffusion equation in the advection-dominated, Peclet-number 10^6 regime. We first demonstrate that, unlike the corresponding physics-informed neural network (PINN), a monolithic NINN can be accurately trained on our model problem without domain decomposition. We then employ overlapping multiplicative Schwarz as a deployment mechanism for coupling a pre-trained, subdomain-local NINN with a neighboring FOM, with the NINN weights held fixed throughout the Schwarz iteration. We consider two training approaches for the subdomain-local NINNs: a top-down approach, in which boundary data are obtained from a coupled Schwarz solve on the full domain with a FOM on each subdomain (FOM-FOM Schwarz), and a bottom-up approach, in which boundary traces are generated synthetically on the NINN subdomain without requiring any full-domain solves. The resulting hybrid NINN-FOM solutions agree closely with the corresponding FOM-FOM Schwarz solutions, with the top-down and bottom-up training approaches yielding comparable accuracy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17841",
  "author_total": 4,
  "authors": [
    {
      "name": "George Chumbipuma"
    },
    {
      "name": "Irina Tezaur"
    },
    {
      "name": "Alejandro Diaz"
    },
    {
      "name": "Beatrice Riviere"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4p5vc39y80y36.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17841",
  "fulltext_url": null,
  "id": "4p5vc39y80y36",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17841",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7213520004",
  "pdf_url": "https://arxiv.org/pdf/2609.17841",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4p5vc39y80y36.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.17841",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17841"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method",
  "title_text": "Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4p5vc39y80y36",
  "venue": "arXiv",
  "versions": []
}