Predicting steady-state behavior in complex networks with graph neural networks.

Area of Science:

• Complex Systems Science
• Network Science
• Machine Learning

Background:

• Information propagation in complex systems can be categorized into diffused, weakly localized, and strongly localized states.
• Understanding these propagation dynamics is crucial for analyzing system behavior.

Purpose of the Study:

• To apply graph neural network (GNN) models for learning and identifying information propagation states in linear dynamical systems on networks.
• To develop a GNN framework capable of accurately distinguishing between different localization states.

Main Methods:

• Development of a graph convolution and attention-based neural network framework.
• Training the GNN model on a linear dynamical system operating on networks.
• Evaluation of the model's performance using both simulated and real-world network data.
• Analytical derivation of the framework's forward and backward propagation for explainability.

Main Results:

• The trained GNN model achieved high accuracy in distinguishing between diffused, weakly localized, and strongly localized information propagation states.
• The model demonstrated robust performance when evaluated on real-world datasets.
• The analytical derivation provided insights into the model's decision-making process.

Conclusions:

• Graph neural networks are effective tools for analyzing information propagation dynamics in complex systems.
• The developed GNN framework offers a powerful and explainable method for state identification.
• This approach has potential applications in various fields involving networked systems.