{
  "abstract": "We investigate the influence of non-dimensionalization on the trainability and accuracy of physics-informed neural networks (PINNs) for buoyancy-driven flows. Using a differentially heated square cavity at $\\mathrm{Pr}=0.71$ and $\\mathrm{Ra}=10^3$--$10^5$, we compare thermal-diffusive and free-fall velocity scalings under identical training conditions. The free-fall scaling, with a unit buoyancy coefficient, achieves errors below 1.1\\% in the mean Nusselt number for $\\mathrm{Ra}\\le10^4$, whereas the diffusive scaling, with a buoyancy coefficient of $\\mathrm{Ra}\\,\\mathrm{Pr}$, produces errors of 157--650\\% and diverges at $\\mathrm{Ra}=10^5$. We identify a coefficient-induced gradient imbalance, with the dominant buoyancy-related contribution to the loss gradient scaling as $(\\mathrm{Ra}\\,\\mathrm{Pr})^2$, and confirm it through direct gradient measurements. Neither sparse-data supervision nor adaptive loss weighting resolves the training difficulties under the tested conditions. For unsteady convection, the free-fall PINN accurately predicts long-time heat transfer but fails to capture the transient Nusselt-number overshoot. These findings establish non-dimensionalization as an important design consideration for improving PINN trainability in buoyancy-driven flows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38889",
  "author_total": 3,
  "authors": [
    {
      "name": "Krishan Chand"
    },
    {
      "name": "Ahmad Peyvan"
    },
    {
      "name": "Haoxiang Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f3fccj9e2awp1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38889",
  "fulltext_url": null,
  "id": "f3fccj9e2awp1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38889",
  "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",
      "physics.flu-dyn"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f3fccj9e2awp1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38889"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Inherent Failure Modes of Physics-Informed Neural Networks for Buoyancy-Driven Flow: Role of Non-Dimensionalization in Network Training",
  "title_text": "Inherent Failure Modes of Physics-Informed Neural Networks for Buoyancy-Driven Flow: Role of Non-Dimensionalization in Network Training",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:45Z",
  "url": "https://research.draconitic.com/paper/f3fccj9e2awp1",
  "venue": "arXiv",
  "versions": []
}