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Graph Neural Ordinary Differential Equations

arXiv 1911.07532 ↗First posted 18 Nov 2019cs.LG cs.AI stat.MLcited by 153

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Abstract (arXiv)

We introduce the framework of continuous--depth graph neural networks (GNNs). Graph neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN layers, blending discrete topological structures and differential equations. The proposed framework is shown to be compatible with various static and autoregressive GNN models. Results prove general effectiveness of GDEs: in static settings they offer computational advantages by incorporating numerical methods in their forward pass; in dynamic settings, on the other hand, they are shown to improve performance by exploiting the geometry of the underlying dynamics.

Key facts. Cited by 153 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Nov 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 10; 2022: 24; 2023: 27; 2024: 37; 2025: 30; 2026: 25.

153 papers.

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  1. 2021GRAND: Graph Neural Diffusioncited by 258
  2. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 246
  3. 2022Graph-Coupled Oscillator Networkscited by 123
  4. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  5. 2024ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEscited by 78
  6. 2021Dissecting the Diffusion Process in Linear Graph Convolutional Networkscited by 58
  7. 2022Anti-Symmetric DGN: a stable architecture for Deep Graph Networkscited by 58
  8. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  9. 2023Effectively Modeling Time Series with Simple Discrete State Spacescited by 54
  10. 2022Gradient Gating for Deep Multi-Rate Learning on Graphscited by 49
  11. 2023A Fractional Graph Laplacian Approach to Oversmoothingcited by 45
  12. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
38 more
  1. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
  2. 2022Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networkscited by 33
  3. 2022ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networkscited by 31
  4. 2024A Review of Graph Neural Networks in Epidemic Modelingcited by 31
  5. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
  6. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  7. 2022Challenges and Opportunities in Deep Reinforcement Learning with Graph Neural Networks: A Comprehensive review of Algorithms and Applicationscited by 27
  8. 2023SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biasescited by 27
  9. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  10. 2024On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systemscited by 26
  11. 2024Long Range Propagation on Continuous-Time Dynamic Graphscited by 26
  12. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  13. 2022Scalable algorithms for physics-informed neural and graph networkscited by 21
  14. 2025Comprehensive Review of Neural Differential Equations for Time Series Analysiscited by 20
  15. 2023Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learningcited by 18
  16. 2022TIDE: Time Derivative Diffusion for Deep Learning on Graphscited by 17
  17. 2023CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systemscited by 16
  18. 2024Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FRONDcited by 16
  19. 2024Topological Neural Networks go Persistent, Equivariant, and Continuouscited by 15
  20. 2024Spiking Graph Neural Network on Riemannian Manifoldscited by 15
  21. 2024Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Seriescited by 14
  22. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  23. 2024Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Responsecited by 13
  24. 2022Modular Flows: Differential Molecular Generationcited by 11
  25. 2024Temporal Graph ODEs for Irregularly-Sampled Time Seriescited by 11
  26. 2022Generalized energy and gradient flow via graph frameletscited by 10
  27. 2022torchode: A Parallel ODE Solver for PyTorchcited by 10
  28. 2023Modulated Neural ODEscited by 10
  29. 2023GNN-based physics solver for time-independent PDEscited by 10
  30. 2024Towards Scene Graph Anticipationcited by 10
  31. 2024Epidemiology-Aware Neural ODE with Continuous Disease Transmission Graphcited by 10
  32. 2023Inferring dynamic regulatory interaction graphs from time series data with perturbationscited by 9
  33. 2024Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Studycited by 9
  34. 2024On The Temporal Domain of Differential Equation Inspired Graph Neural Networkscited by 9
  35. 2024Physics-Informed Regularization for Domain-Agnostic Dynamical System Modelingcited by 9
  36. 2023Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-time Dynamicscited by 8
  37. 2024Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systemscited by 8
  38. 2024Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equationscited by 8

50 most cited of 153 All 153 (JSON)