{
  "abstract": "Deep learning provides a flexible mesh-free framework for solving elliptic interface problems. However, domain-specific neural approaches often rely on separate networks for individual subdomains, causing the model complexity to grow rapidly as the number of subdomains increases. To address this limitation, we propose a Domain-Specific Adaptation Network (DSAN), which combines a shared backbone with lightweight subdomain-specific adapters to provide local represen- representation flexibility without replicating a complete network for each subdomain. We further establish a stability and error analysis showing that the continuous physics-informed residual controls the solution error, and decompose the resulting error into approximation, optimization, and sampling components. Numerical experiments on two- and three-dimensional problems with multiple regular and irregular interfaces demonstrate that DSAN achieves accuracy comparable to or better than fully decomposed multi-network methods while requiring substantially fewer trainable parameters. More- over, the parameter savings become increasingly pronounced as the number of subdomains grows, demonstrating the scalability of the proposed domain-specific adaptation framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14887",
  "author_total": 4,
  "authors": [
    {
      "name": "Jiaqi Luo"
    },
    {
      "name": "Hongmei Kang"
    },
    {
      "name": "Xingye Yue"
    },
    {
      "name": "Shixin Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1f7ew3yh843pq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14887",
  "fulltext_url": null,
  "id": "1f7ew3yh843pq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14887",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.14887",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1f7ew3yh843pq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14887",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14887"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Domain-specific adaptation network for elliptic interface problems",
  "title_text": "A Domain-specific adaptation network for elliptic interface problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1f7ew3yh843pq",
  "venue": "arXiv",
  "versions": []
}