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arXiv 2510.09082cs.AIcs.CYcs.SIphysics.soc-ph
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物理信息驱动的高阶图动力学识别学习用于预测复杂网络长期动力学

Physics-Informed High-order Graph Dynamics Identification Learning for Predicting Complex Networks Long-term Dynamics

State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences(多模态人工智能系统国家重点实验室,自动化研究所,中国科学院);School of Artificial Intelligence, University of Chinese Academy of Sciences(人工智能学院,中国科学院大学)

Bicheng Wang, Junping Wang, Yibo Xue

AI总结:

本文提出一种物理信息驱动的高阶网络动力学识别方法,通过引入动态超图学习捕获非成对关系,并结合Koopman算子与物理信息神经微分方程,实现兼具准确性与可解释性的复杂网络长期动态预测。

摘要:

学习复杂网络动力学是理解、建模和控制现实世界复杂系统的基础。在预测复杂网络动态演化的任务中存在两个主要问题:一方面,现有方法通常使用简单图来描述复杂网络中的关系;然而,这种方法只能捕获成对关系,而网络中可能存在丰富的非成对结构关系。一阶GNN难以捕获动态非成对关系。另一方面,理论预测模型缺乏准确性,而数据驱动的预测模型缺乏可解释性。为了解决上述问题,本文提出了一种用于复杂网络长期动态预测的高阶网络动力学识别方法。首先,针对传统图机器学习只能处理成对关系的问题,引入动态超图学习来捕获复杂网络之间的高阶非成对关系,提高复杂网络建模的准确性。然后,提出了一个物理数据双驱动动态预测模块。引入Koopman算子理论,将复杂网络动态演化的非线性动力学微分方程转化为线性系统进行求解。同时,利用物理信息神经微分方程方法确保动态演化符合物理定律。双驱动动态预测模块确保了预测的准确性和可解释性。在公开数据集和自建的产业链网络数据集上进行验证,实验结果表明本文方法具有良好的预测精度和长期预测性能。

英文摘要:

Learning complex network dynamics is fundamental to understanding, modelling and controlling real-world complex systems. There are two main problems in the task of predicting the dynamic evolution of complex networks: on the one hand, existing methods usually use simple graphs to describe the relationships in complex networks; however, this approach can only capture pairwise relationships, while there may be rich non-pairwise structured relationships in the network. First-order GNNs have difficulty in capturing dynamic non-pairwise relationships. On the other hand, theoretical prediction models lack accuracy and data-driven prediction models lack interpretability. To address the above problems, this paper proposes a higher-order network dynamics identification method for long-term dynamic prediction of complex networks. Firstly, to address the problem that traditional graph machine learning can only deal with pairwise relations, dynamic hypergraph learning is introduced to capture the higher-order non-pairwise relations among complex networks and improve the accuracy of complex network modelling. Then, a dual-driven dynamic prediction module for physical data is proposed. The Koopman operator theory is introduced to transform the nonlinear dynamical differential equations for the dynamic evolution of complex networks into linear systems for solving. Meanwhile, the physical information neural differential equation method is utilised to ensure that the dynamic evolution conforms to the physical laws. The dual-drive dynamic prediction module ensures both accuracy and interpretability of the prediction. Validated on public datasets and self-built industrial chain network datasets, the experimental results show that the method in this paper has good prediction accuracy and long-term prediction performance.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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