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）在关系数据建模方面展现出显著潜力，并已广泛应用于多个重要领域。GNNs的核心机制是所谓的消息传递——信息从邻域节点迭代聚合至中心节点。该过程与被称为热扩散的物理过程存在本质关联，GNNs的信息传播自然对应热密度的演化。将消息传递类比为热动力学，有助于从根本上理解GNNs的优势与局限，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已知局限（如过平滑与过挤压）的工作。本综述首次系统全面地回顾了基于连续视角的GNNs研究。为此，我们介绍了将连续动力学适配至GNNs的基础要素，并提出了图神经动力学的通用设计框架。随后，我们根据驱动机制与底层动力学对现有工作进行梳理与分类，同时总结了连续框架如何解决经典GNNs的局限。最后，我们指出了若干开放的研究方向。