mlsanityData to 7 Oct 2026

Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks

arXiv 2503.23167 ↗First posted 29 Mar 2025cs.LGcited by 14

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Abstract (arXiv)

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

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 108 of its 197 references that are in the map. First posted on arXiv 29 Mar 2025.

Builds on

108 of 197 references.

References · 108

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38 more
  1. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 246
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50 most cited of 108 All 108 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 8; 2026: 6.

14 papers.

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  1. 2025HypKG: Hypergraph-based Knowledge Graph Contextualization for Precision Healthcarecited by 9
  2. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 6
  3. 2025PPG-Distill: Efficient Photoplethysmography Signals Analysis via Foundation Model Distillationcited by 6
  4. 2025Conditional Neural ODE for Longitudinal Parkinson's Disease Progression Forecastingcited by 5
  5. 2025Enabling Group Fairness in Graph Unlearning via Bi-level Debiasingcited by 3
  6. 2025Implicit Hypergraph Neural Networks: A Stable Framework for Higher-Order Relational Learning with Provable Guaranteescited by 3
  7. 2025Discovering Generalizable Governing Equations for Graph Dynamical Systems with Interpretable Neural Networkscited by 1
  8. 2026ECG-MoE: Mixture-of-Expert Electrocardiogram Foundation Modelcited by 1
  9. 2025On the Convergence and Size Transferability of Continuous-depth Graph Neural Networkscited by 0
  10. 2026Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEscited by 0
  11. 2026Exposing Vulnerabilities in Explanation for Time Series Classifiers via Dual-Target Attackscited by 0
  12. 2026Lyapunov Stable Graph Neural Flowcited by 0
2 more
  1. 2026Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitionscited by 0
  2. 2026INDEQS: Informed Neural controlled Differential EQuationScited by 0