图神经常微分方程综述

Survey on Graph Neural Ordinary Differential Equations

图神经网络(graph neural network,GNN)是处理图结构数据的强大工具,能够捕捉节点间的复杂关系和特征.但GNN的离散架构导致其在表示图结构、建模图演化、适应不规则数据和计算开销等方面面临诸多挑战.面对这些挑战,神经常微分方程(ordinary differential equation,ODE)由于能够模拟系统状态的连续变化,具备“连续深度”的编码和推断能力,被作为解决GNN面临挑战的全新方法而引入.然而,神经ODE是为欧式结构数据设计的,无法直接捕捉图结构特性.因此,提出了图神经ODE,一种将神经ODE与GNN结合的新架构,可以更好地适应图结构数据并充分利用其特性.近年来,图神经ODE相关研究已经深入到图机器学习的各个方向中,引发了新的研究热潮.在此背景下,适时地对图神经ODE研究前沿进行了系统性综述.首先,回顾了GNN的关键优势和面临的诸多挑战,阐述了引入神经ODE并与GNN结合的理论基础和实践意义.随后,详细介绍了图神经ODE的背景和基本概念,并提出了一种新颖的分类方法,在此基础上对当前的相关方法进行了全面描述.然后,介绍了相关研究常用的验证方法,包括下游任务及数据集.进一步,深入探讨了图神经ODE在多个实用领域上的应用.最后,对图神经ODE面临的挑战和未来发展趋势进行了总结和展望.

Graph neural networks(GNNs)are powerful tools for handling graph-structured data,capable of capturing complex relationships and features among nodes.However,the discrete architecture of GNNs leads to numerous challenges in representing graph structures,modeling graph evolution,adapting to irregular data,and managing computational costs.In response to these challenges,neural ordinary differential equations(ODEs)have been introduced as a novel method to address the challenges faced by GNNs,as they can simulate the continuous evolution of system states,providing continuous deep encoding and inference capabilities.However,neural ODEs are designed for Euclidean structured data and cannot directly capture the characteristics of graphs.Therefore,researchers have proposed graph neural ODEs,a new type of architectures that combines neural ODEs with GNNs,which can better adapt to graph-structured data and fully utilize its characteristics.In recent years,research related to graph neural ODEs has delved into various directions of graph machine learning,sparking a new research trend.In this context,we systematically review the relevant research of graph neural ODEs in a timely manner.Firstly,we review the key advantages of GNNs and the challenges they face,and elucidate the theoretical basis and practical significance of introducing neural ODEs and combining them with GNNs.Subsequently,we elaborate on the background and basic concepts of graph neural ODEs,proposing a novel taxonomy,and comprehensively describe some important current methods on the taxonomy.Then,we introduce commonly used verification methods in related research,including downstream tasks and datasets.Furthermore,we delve into the applications of graph neural ODEs in multiple practi-cal fields.Finally,we summarize and prospect the challenges and future development trends of graph neural ODEs.