{
  "abstract": "Finite-volume extrapolation (FVE) is essential for extracting physical observables in the lattice calculation. While rigorous FVE formulations are well established for short-range potentials in both two- and three-body systems, long-range interactions with force ranges comparable to the lattice size $L$ remain challenging. Extending a previous data-driven scheme for two-body systems, we apply symbolic regression (PySR) to uncover universal three-body FVE formulae. For short-range potentials, we reproduce the two limiting cases, i.e. $κ_3\\ggκ_2$ and $κ_3\\simκ_2$. For pure long-range potentials, we obtain a dedicated analytic expression, and after incorporating short-range contributions, we uncover a unified formula consistent with the original PySR solution, which performs excellently in the intermediate force range around 1 fm. This work demonstrates that combining machine learning with physical constraints can yield novel analytical results inaccessible to conventional theoretical tools, advancing data-driven methodologies in hadron physics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28700",
  "author_total": 6,
  "authors": [
    {
      "name": "Wei-Jie Zhang"
    },
    {
      "name": "Zhenyu Zhang"
    },
    {
      "name": "Jifeng Hu"
    },
    {
      "name": "Bing-Nan Lu"
    },
    {
      "name": "Jin-Yi Pang"
    },
    {
      "name": "Qian Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/156f3zcy9qemt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28700",
  "fulltext_url": null,
  "id": "156f3zcy9qemt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28700",
  "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",
      "hep-lat"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7204882929",
  "pdf_url": "https://arxiv.org/pdf/2608.28700",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/156f3zcy9qemt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.28700",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28700"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Machine Learning Unveils Finite-volume Energy Shifts in Three-body System",
  "title_text": "Machine Learning Unveils Finite-volume Energy Shifts in Three-body System",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/156f3zcy9qemt",
  "venue": "arXiv",
  "versions": []
}