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

2025-10-10

AI Summary

Addressing the dual challenges of modeling high-order, non-pairwise interactions in long-term dynamic prediction of complex networks and balancing accuracy with interpretability, this paper proposes a physics-guided dynamic hypergraph learning framework. Methodologically: (1) we design a dynamic hypergraph neural network to explicitly capture high-order collaborative relationships among nodes; (2) we integrate Koopman operator theory with physics-informed neural differential equations (PINNs) to develop a hybrid physics- and data-driven prediction module, embedding dynamical priors while preserving forecasting accuracy. Experiments on public benchmarks and real-world industrial chain networks demonstrate that our approach significantly improves long-term prediction accuracy (reducing average error by 23.6%) and temporal stability, while exhibiting strong generalization capability and intrinsic interpretability. This work establishes a novel paradigm for modeling complex dynamical systems.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

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.

Problem

• Capturing higher-order non-pairwise relationships in complex networks
• Improving accuracy and interpretability of network dynamics prediction
• Transforming nonlinear dynamics into linear systems using Koopman theory

Innovation

• Dynamic hypergraph learning captures higher-order non-pairwise relationships
• Koopman operator transforms nonlinear dynamics into linear systems
• Physical information neural differential equations enforce physical law compliance