{
  "abstract": "We present a physics--informed neural solver for the generalized Falkner--Skan boundary-value problem that combines an exact boundary--admissible trial representation with adaptive regional residual balancing (ARRB). The three prescribed boundary conditions are embedded analytically, eliminating boundary-condition penalty terms while allowing the finite--domain streamfunction value and wall shear to be determined by the governing equation. The residual is divided into wall, middle, and tail regions, and a physical global residual is reconstructed from regional mean-squared errors using region-length fractions. Safeguarded exponential--moving--average inverse--gradient coefficients adaptively balance the regional contributions during Adam optimization. A deterministic 800-point residual monitor is used for checkpoint selection, followed by two deterministic L--BFGS stages minimizing the physical global residual. The method is tested on the Blasius, favourable-pressure--gradient Falkner--Skan, and Pohlhausen cases. For \\((β_0,β_1)=(0.75,0.50)\\), the predicted wall shear is \\(f''(0)=0.8997161394\\), compared with the finite-domain reference \\(0.8997168085\\), giving an absolute error of \\(6.691\\times10^{-7}\\). The residual MSE is \\(6.357\\times10^{-9}\\), while the relative \\(L_2\\) errors in \\(f'\\) and \\(f''\\) are \\(2.848\\times10^{-6}\\) and \\(4.188\\times10^{-5}\\). A matched single--seed ablation shows that ARRB reduces residual MSE by 52.81\\% relative to global--residual training and by 50.24\\% relative to equal-regional weighting. Wall--shear errors are reduced by 77.30\\% and 72.37\\%, respectively. These results support ARRB as an accuracy-oriented residual-conditioning strategy, while multi--seed experiments remain necessary to quantify optimization variability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23493",
  "author_total": 2,
  "authors": [
    {
      "name": "Mehari Fentahun Endalew"
    },
    {
      "name": "Xiaoming John Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5887kvcr53m5a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23493",
  "fulltext_url": null,
  "id": "5887kvcr53m5a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23493",
  "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",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7214014430",
  "pdf_url": "https://arxiv.org/pdf/2609.23493",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5887kvcr53m5a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23493",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23493"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Hard-Constrained Physics--Informed Neural Network with Adaptive Regional Residual Balancing for the Generalized Falkner--Skan Problem",
  "title_text": "Hard-Constrained Physics--Informed Neural Network with Adaptive Regional Residual Balancing for the Generalized Falkner--Skan Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/5887kvcr53m5a",
  "venue": "arXiv",
  "versions": []
}