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Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks
Zewen Liu1, Xiaoda Wang1, Bohan Wang1
1Emory University, Atlanta, GA, USA.
KDD : Proceedings. International Conference on Knowledge Discovery & Data Mining
|August 21, 2025
Summary
Graph Neural Networks (GNNs) and differential equations (DEs) offer powerful synergy for scientific modeling. This survey explores their combined use in areas like physics-informed learning and spatiotemporal prediction.
Area of Science:
- Artificial Intelligence
- Computational Science
- Applied Mathematics
Background:
- Graph Neural Networks (GNNs) excel at learning from graph-structured data.
- Differential Equations (DEs) provide a robust framework for modeling continuous dynamics.
- Recent advancements reveal significant synergy between GNNs and DEs.
Purpose of the Study:
- To provide a comprehensive overview of research at the intersection of GNNs and DEs.
- To categorize existing methods and discuss their underlying principles.
- To highlight applications and identify future research directions.
Main Methods:
- Surveying and categorizing existing literature on GNNs and DEs.
- Analyzing the integration of GNNs for solving or learning DEs.
- Examining applications across diverse scientific domains.
Main Results:
- Identification of innovative approaches leveraging GNNs and DEs.
- Demonstration of applications in physics-informed learning, spatiotemporal modeling, and scientific computing.
- Categorization of methods based on their integration strategies.
Conclusions:
- The intersection of GNNs and DEs is a rapidly advancing interdisciplinary field.
- This synergy enables powerful solutions for complex scientific problems.
- Further research is needed to address open challenges and unlock new potential.
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