{
  "abstract": "Rarefied nonequilibrium flows are described by the Boltzmann equation, which can be solved using stochastic particle or deterministic methods. With advances in computing, data-assisted physics-informed neural networks have been widely used for flow prediction by combining governing equations with measured or computed data. Data-free PINNs do not require such training data and have been widely studied for continuum flows, but their application to rarefied flows remains limited. This study develops a data-free Fokker-Planck physics-informed neural network (FP-PINN) to describe rarefied nonequilibrium flows. The physics loss is constructed from the ellipsoidal statistical Fokker-Planck (ES-FP) equation using a velocity distribution function (VDF) closure and moment projection. The FP-PINN is evaluated for a steady one-dimensional Mach 10 normal shock. The FP-PINN results agree with the numerical ES-FP results, with errors below $1\\%$. Compared with the particle ES-FP results, the FP-PINN predicts a sharper shock structure with errors up to $17\\%$. This difference is attributed to the VDF closure and moment projection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22390",
  "author_total": 2,
  "authors": [
    {
      "name": "Joonbeom Kim"
    },
    {
      "name": "Eunji Jun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6xw30yraqz8fc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22390",
  "fulltext_url": null,
  "id": "6xw30yraqz8fc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22390",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7222967014",
  "pdf_url": "https://arxiv.org/pdf/2610.22390",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6xw30yraqz8fc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.22390",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22390"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Physics-informed Neural Networks Based on the Fokker-Planck Model for Rarefied Gas Flows",
  "title_text": "Physics-informed Neural Networks Based on the Fokker-Planck Model for Rarefied Gas Flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/6xw30yraqz8fc",
  "venue": "arXiv",
  "versions": []
}