{
  "abstract": "We study free-boundary problems within a physics-informed framework using Kolmogorov-Arnold network (KAN) approximations. The proposed approach incorporates obstacle constraints, partial differential equation (PDE) inequalities, complementarity conditions, and boundary conditions through residual-based loss functions. We consider a linear elliptic obstacle problem, a nonlinear $p$-Laplacian obstacle problem, and a time-dependent one-phase Stefan problem. The proposed KAN solver is compared with physics-informed neural network (PINN) and residual-network baselines. Numerical experiments show that KANs achieve low relative $L^2$ and $L^\\infty$ errors while accurately resolving contact regions and moving interfaces. The results indicate that KAN representations provide an effective alternative for solving free-boundary PDEs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02084",
  "author_total": 1,
  "authors": [
    {
      "name": "Tan Phuong Dong Le"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c5pn12hv7391b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02084",
  "fulltext_url": null,
  "id": "c5pn12hv7391b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02084",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7216567293",
  "pdf_url": "https://arxiv.org/pdf/2610.02084",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c5pn12hv7391b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02084",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02084"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Kolmogorov-Arnold Networks for Free-Boundary Partial Differential Equations",
  "title_text": "Kolmogorov-Arnold Networks for Free-Boundary Partial Differential Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/c5pn12hv7391b",
  "venue": "arXiv",
  "versions": []
}