{
  "abstract": "Phase-field equations are fundamental examples of gradient-flow systems and require numerical solvers that preserve intrinsic energy dissipation. In this work, we propose a neural network-based method that combines an SAV time discretization with a mesh-free neural representation. We establish the unconditional energy stability of the underlying SAV semi-discretization, quantify the energy defect caused by solver residuals, and derive a conditional high-probability error estimate for the Allen--Cahn equation. Numerical experiments show that our approach consistently exhibits energy-stable behavior, while outperforming existing neural network-based solvers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08088",
  "author_total": 3,
  "authors": [
    {
      "name": "Tao Luo"
    },
    {
      "name": "Guihong Wang"
    },
    {
      "name": "Wei Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ht7ggmvk753d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08088",
  "fulltext_url": null,
  "id": "2ht7ggmvk753d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08088",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7220924824",
  "pdf_url": "https://arxiv.org/pdf/2610.08088",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ht7ggmvk753d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08088",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08088"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A SAV Neural Network Method for Allen--Cahn and Cahn--Hilliard Equations",
  "title_text": "A SAV Neural Network Method for Allen--Cahn and Cahn--Hilliard Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/2ht7ggmvk753d",
  "venue": "arXiv",
  "versions": []
}