  Neural diffusion on graphs is a novel class of graph neural networks that has
attracted increasing attention recently. The capability of graph neural partial
differential equations (PDEs) in addressing common hurdles of graph neural
networks (GNNs), such as the problems of over-smoothing and bottlenecks, has
been investigated but not their robustness to adversarial attacks. In this
work, we explore the robustness properties of graph neural PDEs. We empirically
demonstrate that graph neural PDEs are intrinsically more robust against
topology perturbation as compared to other GNNs. We provide insights into this
phenomenon by exploiting the stability of the heat semigroup under graph
topology perturbations. We discuss various graph diffusion operators and relate
them to existing graph neural PDEs. Furthermore, we propose a general graph
neural PDE framework based on which a new class of robust GNNs can be defined.
We verify that the new model achieves comparable state-of-the-art performance
on several benchmark datasets.
