Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is being iteratively aggregated to central nodes from their neighbourhood. Such a scheme has been found to be intrinsically linked to a physical process known as heat diffusion, where the propagation of GNNs naturally corresponds to the evolution of heat density. Analogizing the process of message passing to the heat dynamics allows to fundamentally understand the power and pitfalls of GNNs and consequently informs better model design. Recently, there emerges a plethora of works that proposes GNNs inspired from the continuous dynamics formulation, in an attempt to mitigate the known limitations of GNNs, such as oversmoothing and oversquashing. In this survey, we provide the first systematic and comprehensive review of studies that leverage the continuous perspective of GNNs. To this end, we introduce foundational ingredients for adapting continuous dynamics to GNNs, along with a general framework for the design of graph neural dynamics. We then review and categorize existing works based on their driven mechanisms and underlying dynamics. We also summarize how the limitations of classic GNNs can be addressed under the continuous framework. We conclude by identifying multiple open research directions.

翻译：图神经网络（GNNs）在关系型数据建模方面展现出显著潜力，并已广泛应用于多个研究领域。其核心机制是消息传递——信息通过迭代方式从邻域节点向中心节点聚合。该机制本质上与物理中的热扩散过程存在内在关联，GNNs的信息传播自然对应于热密度的演化。将消息传递过程类比为热动力学，有助于从根本上理解GNNs的能力与局限性，从而指导更优的模型设计。近年来，受连续动力学公式启发，涌现出大量旨在缓解GNNs已知缺陷（如过平滑与过挤压问题）的研究。本综述首次系统全面地梳理了基于连续视角研究GNNs的相关工作。为此，我们引入将连续动力学适配至GNNs的基础要素，并构建了图神经动力学设计通用框架。随后，根据驱动机制和底层动力学对现有工作进行分类评述，同时总结连续框架如何解决经典GNNs的局限性。最后，我们指出多个有待探索的开放研究方向。