整合微分方程与图神经网络，提升复杂系统建模能力
Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks
- 将微分方程思想融入图神经网络，实现连续动态建模
- 在分子、交通、疫情等场景中展现优越性能
- 适合对物理信息学习和时空建模感兴趣的研究者
图神经网络（GNNs）与微分方程（DEs）是近年来快速发展的两个研究领域，二者展现出显著的协同效应。GNNs已成为处理图结构数据的强大工具，而微分方程则为时间与空间上的连续动态建模提供了严谨框架。两者的结合催生了创新方法，充分发挥各自优势，广泛应用于物理信息学习、时空建模及科学计算等领域。本综述全面梳理了该交叉领域的研究进展，分类归纳现有方法，阐述其核心原理，并展示其在分子建模、交通预测、疫情传播等领域的应用。同时，识别出关键挑战并提出未来研究方向。完整论文列表见 https://github.com/Emory-Melody/Awesome-Graph-NDEs。本文为希望理解并参与图神经网络与微分方程融合研究的研究人员与实践者提供重要参考。
原文摘要 · Abstract (English)
Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while differential equations provide a principled framework for modeling continuous dynamics across time and space. The intersection of these fields has led to innovative approaches that leverage the strengths of both, enabling applications in physics-informed learning, spatiotemporal modeling, and scientific computing. This survey aims to provide a comprehensive overview of the burgeoning research at the intersection of GNNs and DEs. We will categorize existing methods, discuss their underlying principles, and highlight their applications across domains such as molecular modeling, traffic prediction, and epidemic spreading. Furthermore, we identify open challenges and outline future research directions to advance this interdisciplinary field. A comprehensive paper list is provided at https://github.com/Emory-Melody/Awesome-Graph-NDEs. This survey serves as a resource for researchers and practitioners seeking to understand and contribute to the fusion of GNNs and DEs
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。