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

arXiv: https://arxiv.org/abs/2503.23167 · HTML: https://mlsanity.com/paper/2503.23167/

## Key facts

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

## Builds on (most cited first, 30 of 108)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs](https://mlsanity.com/paper/2202.08408/) (2022)
- [Label-free Node Classification on Graphs with Large Language Models (LLMS)](https://mlsanity.com/paper/2310.04668/) (2023)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [Temporal Knowledge Graph Forecasting with Neural ODE](https://mlsanity.com/paper/2101.05151/) (2021)
- [Anti-Symmetric DGN: a stable architecture for Deep Graph Networks](https://mlsanity.com/paper/2210.09789/) (2022)

## Built on by (most cited first, 14 of 14)

- [Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme](https://mlsanity.com/paper/2506.01502/) (2025)
- [HypKG: Hypergraph-based Knowledge Graph Contextualization for Precision Healthcare](https://mlsanity.com/paper/2507.19726/) (2025)
- [PPG-Distill: Efficient Photoplethysmography Signals Analysis via Foundation Model Distillation](https://mlsanity.com/paper/2509.19215/) (2025)
- [Conditional Neural ODE for Longitudinal Parkinson's Disease Progression Forecasting](https://mlsanity.com/paper/2511.04789/) (2025)
- [Enabling Group Fairness in Graph Unlearning via Bi-level Debiasing](https://mlsanity.com/paper/2505.09702/) (2025)
- [Implicit Hypergraph Neural Networks: A Stable Framework for Higher-Order Relational Learning with Provable Guarantees](https://mlsanity.com/paper/2508.09427/) (2025)
- [Discovering Generalizable Governing Equations for Graph Dynamical Systems with Interpretable Neural Networks](https://mlsanity.com/paper/2508.18173/) (2025)
- [On the Convergence and Size Transferability of Continuous-depth Graph Neural Networks](https://mlsanity.com/paper/2510.03923/) (2025)
- [ECG-MoE: Mixture-of-Expert Electrocardiogram Foundation Model](https://mlsanity.com/paper/2603.04589/) (2026)
- [Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs](https://mlsanity.com/paper/2601.11259/) (2026)
- [Exposing Vulnerabilities in Explanation for Time Series Classifiers via Dual-Target Attacks](https://mlsanity.com/paper/2602.02763/) (2026)
- [Lyapunov Stable Graph Neural Flow](https://mlsanity.com/paper/2603.12557/) (2026)
- [Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitions](https://mlsanity.com/paper/2604.24293/) (2026)
- [INDEQS: Informed Neural controlled Differential EQuationS](https://mlsanity.com/paper/2606.19138/) (2026)

## 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