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

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.