Discovering hierarchical governing equations for community-structured complex network dynamics with LLM agents

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.

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Cite

BibTeX RIS

BibTeX

@misc{zhang2026discovering,
  title = {{Discovering hierarchical governing equations for community-structured complex network dynamics with LLM agents}},
  author = {Jinlei Zhang and Zixuan Zhang and Hao Qiu and Feng Chen and Jiateng Yin and Xiaoyong Yan and Xiaolei Ma and Hao Sun and Jianxi Gao and Lixing Yang and Ziyou Gao},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02816},
  eprint = {2611.02816},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02816},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - Discovering hierarchical governing equations for community-structured complex network dynamics with LLM agents
AU  - Jinlei Zhang
AU  - Zixuan Zhang
AU  - Hao Qiu
AU  - Feng Chen
AU  - Jiateng Yin
AU  - Xiaoyong Yan
AU  - Xiaolei Ma
AU  - Hao Sun
AU  - Jianxi Gao
AU  - Lixing Yang
AU  - Ziyou Gao
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02816
UR  - https://arxiv.org/abs/2611.02816
AB  - 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.
ER  -

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