{
  "abstract": "This paper develops a deep learning framework for solving high-dimensional stationary Fokker-Planck equations by combining Monte Carlo weak supervision, energy-variational physics constraints, and quasi-Newton refinement. Monte Carlo statistics anchor the scale of the stationary density, while a free-energy variational loss enforces equilibrium physics; the formulation also applies to stationary systems with pointwise orthogonal rotational components and, using a family of test functions, to systems with more general non-gradient drift. Numerical results demonstrate accurate and robust density approximations across a range of high-dimensional stationary Fokker-Planck problems, including rough-potential and noisy-data settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03325",
  "author_total": 3,
  "authors": [
    {
      "name": "Fanze Kong"
    },
    {
      "name": "Zhouyuan Qin"
    },
    {
      "name": "Shuangquan Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b49n3eqpr5ggr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03325",
  "fulltext_url": null,
  "id": "b49n3eqpr5ggr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03325",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.03325",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b49n3eqpr5ggr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03325",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03325"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Energetic Variational Deep Learning for Solving High-Dimensional Stationary Fokker-Planck Equations",
  "title_text": "Energetic Variational Deep Learning for Solving High-Dimensional Stationary Fokker-Planck Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/b49n3eqpr5ggr",
  "venue": "arXiv",
  "versions": []
}