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

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.