Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks
It synthesizes interdisciplinary research for researchers and practitioners in fields like molecular modeling and traffic prediction, but is incremental as a survey.
This survey tackles the problem of integrating graph neural networks (GNNs) with differential equations (DEs) to enhance modeling of graph-structured data, providing a comprehensive overview of methods, applications, and future directions without presenting new experimental results.
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