{
  "abstract": "A controlled comparative study of a mesh-free Kolmogorov--Arnold Physics-Informed Neural Network (KAN-PINN) applied to nonlinear strain-limiting partial differential equations is presented. Three distinct training runs across varying material-parameter pairs $(α, β)$ are evaluated within a fixed computational pipeline comprising an exact hard boundary ansatz, a robust pseudo-Huber residual loss, and a multi-stage Adam-to-L-BFGS optimizer schedule. A fundamental metric inversion is revealed by the analysis: while training loss reflects operator-specific residual scaling and constitutive stiffness, the operator-independent relative $L_2$ error demonstrates that intermediate parameter regimes achieve superior solution accuracy and enhanced generalization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25507",
  "author_total": 1,
  "authors": [
    {
      "name": "B. Veena S. N. Rao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/49m90kd25zsej.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25507",
  "fulltext_url": null,
  "id": "49m90kd25zsej",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25507",
  "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.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7214113851",
  "pdf_url": "https://arxiv.org/pdf/2609.25507",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/49m90kd25zsej.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25507",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25507"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "AKAPINN: Adaptive Kolmogorov-Arnold Physics-Informed Neural Networks for approximating solutions to quasilinear partial differential equations",
  "title_text": "AKAPINN: Adaptive Kolmogorov-Arnold Physics-Informed Neural Networks for approximating solutions to quasilinear partial differential equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/49m90kd25zsej",
  "venue": "arXiv",
  "versions": []
}