Predicting Steady-State Behavior in Complex Networks with Graph Neural Networks

TL;DR

This paper introduces a graph neural network framework to predict the steady-state behavior of linear dynamical systems on complex networks, demonstrating high accuracy and explainability with real-world data.

Contribution

The study develops a novel GNN-based model that accurately predicts steady states and provides analytical insights into its propagation mechanisms.

Findings

High accuracy in distinguishing different states

Effective performance on real-world network data

Analytical derivation enhances model explainability

Abstract

In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear dynamical system on networks. A graph convolution and attention-based neural network framework has been developed to identify the steady-state behavior of the linear dynamical system. We reveal that our trained model distinguishes the different states with high accuracy. Furthermore, we have evaluated model performance with real-world data. In addition, to understand the explainability of our model, we provide an analytical derivation for the forward and backward propagation of our framework.