Feature Transportation Improves Graph Neural Networks

Graph neural networks (GNNs) have shown remarkable success in learning representations for graph-structured data. However, GNNs still face challenges in modeling complex phenomena that involve feature transportation. In this paper, we propose a novel GNN architecture inspired by Advection-Diffusion-Reaction systems, called ADR-GNN. Advection models feature transportation, while diffusion captures the local smoothing of features, and reaction represents the nonlinear transformation between feature channels. We provide an analysis of the qualitative behavior of ADR-GNN, that shows the benefit of combining advection, diffusion, and reaction. To demonstrate its efficacy, we evaluate ADR-GNN on real-world node classification and spatio-temporal datasets, and show that it improves or offers competitive performance compared to state-of-the-art networks.