{
  "abstract": "Governing equations provide an interpretable description of the mechanisms underlying complex network dynamics, yet their discovery from observational data remains challenging when shared community-level dynamics coexist with individual-level variations and the relevant functional structures may be absent from the initial candidate library or not explicitly specified in advance. Here we formulate this task as a hierarchical law-discovery problem and introduce SAGE, a large language model-guided self-reflective agent framework for discovering community-shared governing laws and individual-specific dynamical variations. SAGE organizes equation discovery into an iterative Library-Discovery-Review process that first identifies shared community-level structures and then resolves node-specific residual dynamics, while adaptively refining the candidate space to introduce missing dynamical terms when needed. This hierarchical and interpretable formulation enables SAGE to distinguish shared community-level dynamics from individual-level variations and to reveal the mechanisms underlying complex network dynamics. Across two synthetic networks and four real-world networks spanning mobile communication, brain electrophysiology, power grids and urban rail transit, SAGE recovers compact and interpretable governing equations, reproduces observed system dynamics and outperforms representative equation-discovery baselines. The framework remains robust under incomplete observations and can transfer community-level governing laws to nodes with entirely missing observations. These results establish a hierarchical and adaptive approach for disentangling shared and individual dynamical mechanisms in community-structured complex networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02816",
  "author_total": 11,
  "authors": [
    {
      "name": "Jinlei Zhang"
    },
    {
      "name": "Zixuan Zhang"
    },
    {
      "name": "Hao Qiu"
    },
    {
      "name": "Feng Chen"
    },
    {
      "name": "Jiateng Yin"
    },
    {
      "name": "Xiaoyong Yan"
    },
    {
      "name": "Xiaolei Ma"
    },
    {
      "name": "Hao Sun"
    },
    {
      "name": "Jianxi Gao"
    },
    {
      "name": "Lixing Yang"
    },
    {
      "name": "Ziyou Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56frwz5eja21v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02816",
  "fulltext_url": null,
  "id": "56frwz5eja21v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02816",
  "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",
      "cs.AI"
    ],
    [
      "arxiv",
      "physics.soc-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02816",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56frwz5eja21v.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02816",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02816"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Discovering hierarchical governing equations for community-structured complex network dynamics with LLM agents",
  "title_text": "Discovering hierarchical governing equations for community-structured complex network dynamics with LLM agents",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/56frwz5eja21v",
  "venue": "arXiv",
  "versions": []
}