  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 non-linear 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.
