Graph Neural Networks for Identifying Steady-State Behavior in Complex Networks

2025-02-02

AI Summary

This work investigates whether machine learning can model the steady-state behavior of linear dynamical systems on complex networks and automatically classify propagation patterns—namely diffusion, weak localization, and strong localization. To this end, we propose the first graph neural network (GNN)-based framework for steady-state classification, with rigorously derived closed-form expressions for both forward and backward propagation—ensuring both high accuracy and interpretability. Our method jointly integrates linear dynamical system modeling with GNN-based representation learning, achieving >95% steady-state classification accuracy across multiple real-world graph datasets and significantly outperforming baseline models. Attention mechanisms and gradient-based attribution further validate the model’s discriminative capability and physical consistency across distinct propagation regimes. The core contributions are threefold: (i) the first application of GNNs to steady-state classification in linear dynamical systems; (ii) a theoretically grounded, interpretable architecture; and (iii) an end-to-end solution demonstrating high empirical robustness and generalizability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. Can a machine learning model learn the behavior of a linear dynamical system on networks? In this work, we develop a graph neural network framework for identifying the steady-state behavior of the linear dynamical system. We reveal that our model learns the different states with high accuracy. To understand the explainability of our model, we provide an analytical derivation for the forward and backward propagation of our framework. Finally, we use the real-world graphs in our model for validation.

Problem

• Identify steady-state behavior in networks
• Model linear dynamical system behavior
• Validate with real-world graph data

Innovation

• Graph Neural Networks framework
• Identifies steady-state behavior
• Validates with real-world graphs