{
  "abstract": "Stokes-Brinkman-Darcy (SBD) models connect free flow and porous flow through a Brinkman layer of finite thickness. The proposed method for solving these coupled equations consists of a mixed first-order formulation, shared interface traces and hard traction constraints, and a pressure correction based on boundary mass balance. Independent stresses, Darcy flux and pressure-gradient auxiliaries avoid second derivatives of network outputs. Boundary liftings and shared traces impose exterior and interface kinematic conditions exactly, while a stress map enforces native Brinkman-Darcy force balance. An integral momentum relation determines the pressure correction after training, without reference-pressure labels. Across two manufactured solutions and three permeabilities, mean corrected upper-pressure relative $L^2$ errors range from 0.87% to 2.58%; correction reduces both upper-pressure $L^2$ errors and the full Brinkman-pressure $H^1$ error in every run. Paired controls assess the contributions of interface sharing and traction enforcement. A non-manufactured filtration problem tests mixed-boundary adaptation against an independently refined finite-element reference, with all four runs satisfying the prescribed field and physical-consistency criteria.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36793",
  "author_total": 2,
  "authors": [
    {
      "name": "Zefeng Liu"
    },
    {
      "name": "Hongxing Rui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4pgjzyn2xwg1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36793",
  "fulltext_url": null,
  "id": "d4pgjzyn2xwg1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36793",
  "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"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7214975782",
  "pdf_url": "https://arxiv.org/pdf/2609.36793",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4pgjzyn2xwg1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36793",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36793"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Hard-Trace First-Order Residual Learning for Coupled Stokes-Brinkman-Darcy Flow",
  "title_text": "Hard-Trace First-Order Residual Learning for Coupled Stokes-Brinkman-Darcy Flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/d4pgjzyn2xwg1",
  "venue": "arXiv",
  "versions": []
}