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Graph neural networks (GNNs) have demonstrated significant promise inmodelling relational data and have been widely applied in various fields ofinterest. The key mechanism behind GNNs is the so-called message passing whereinformation is being iteratively aggregated to central nodes from theirneighbourhood. Such a scheme has been found to be intrinsically linked to aphysical process known as heat diffusion, where the propagation of GNNsnaturally corresponds to the evolution of heat density. Analogizing the processof message passing to the heat dynamics allows to fundamentally understand thepower and pitfalls of GNNs and consequently informs better model design.Recently, there emerges a plethora of works that proposes GNNs inspired fromthe continuous dynamics formulation, in an attempt to mitigate the knownlimitations of GNNs, such as oversmoothing and oversquashing. In this survey,we provide the first systematic and comprehensive review of studies thatleverage the continuous perspective of GNNs. To this end, we introducefoundational ingredients for adapting continuous dynamics to GNNs, along with ageneral framework for the design of graph neural dynamics. We then review andcategorize existing works based on their driven mechanisms and underlyingdynamics. We also summarize how the limitations of classic GNNs can beaddressed under the continuous framework. We conclude by identifying multipleopen research directions.

From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond