# Neural Dynamics on Complex Networks

arXiv: https://arxiv.org/abs/1908.06491 · HTML: https://mlsanity.com/paper/1908.06491/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2019.

## Built on by (most cited first, 30 of 38)

- [Understanding convolution on graphs via energies](https://mlsanity.com/paper/2206.10991/) (2022)
- [Attentive Neural Controlled Differential Equations for Time-series Classification and Forecasting](https://mlsanity.com/paper/2109.01876/) (2021)
- [Generalizing Graph ODE for Learning Complex System Dynamics across Environments](https://mlsanity.com/paper/2307.04287/) (2023)
- [Climate Modeling with Neural Diffusion Equations](https://mlsanity.com/paper/2111.06011/) (2021)
- [CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems](https://mlsanity.com/paper/2306.11216/) (2023)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Temporal Graph ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/2404.19508/) (2024)
- [Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling](https://mlsanity.com/paper/2410.06366/) (2024)
- [Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-time Dynamics](https://mlsanity.com/paper/2312.11198/) (2023)
- [Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systems](https://mlsanity.com/paper/2403.00178/) (2024)
- [Learning Dynamic Graph Embeddings with Neural Controlled Differential Equations](https://mlsanity.com/paper/2302.11354/) (2023)
- [ConTIG: Continuous Representation Learning on Temporal Interaction Graphs](https://mlsanity.com/paper/2110.06088/) (2021)
- [Learning Locally Interacting Discrete Dynamical Systems: Towards Data-Efficient and Scalable Prediction](https://mlsanity.com/paper/2404.06460/) (2024)
- [Continuous Temporal Graph Networks for Event-Based Graph Data](https://mlsanity.com/paper/2205.15924/) (2022)
- [Learning Modular Simulations for Homogeneous Systems](https://mlsanity.com/paper/2210.16294/) (2022)
- [TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems](https://mlsanity.com/paper/2310.06427/) (2023)
- [Learning Interpretable Network Dynamics via Universal Neural Symbolic Regression](https://mlsanity.com/paper/2411.06833/) (2024)
- [Do We Need an Encoder-Decoder to Model Dynamical Systems on Networks?](https://mlsanity.com/paper/2305.12185/) (2023)
- [Learning the effective order of a hypergraph dynamical system](https://mlsanity.com/paper/2306.01813/) (2023)
- [TDNetGen: Empowering Complex Network Resilience Prediction with Generative Augmentation of Topology and Dynamics](https://mlsanity.com/paper/2408.09825/) (2024)
- [Online Relational Inference for Evolving Multi-agent Interacting Systems](https://mlsanity.com/paper/2411.01442/) (2024)
- [UniGO: A Unified Graph Neural Network for Modeling Opinion Dynamics on Graphs](https://mlsanity.com/paper/2502.11519/) (2025)
- [Learning Continuous Network Emerging Dynamics from Scarce Observations via Data-Adaptive Stochastic Processes](https://mlsanity.com/paper/2310.16466/) (2023)
- [R-ODE: Ricci Curvature Tells When You Will be Informed](https://mlsanity.com/paper/2405.17282/) (2024)
- [Neural Symbolic Regression of Complex Network Dynamics](https://mlsanity.com/paper/2410.11185/) (2024)
- [Graph Fourier Neural ODEs: Modeling Spatial-temporal Multi-scales in Molecular Dynamics](https://mlsanity.com/paper/2411.01600/) (2024)
- [Remember Past, Anticipate Future: Learning Continual Multimodal Misinformation Detectors](https://mlsanity.com/paper/2507.05939/) (2025)
- [A Stage-Aware Mixture of Experts Framework for Neurodegenerative Disease Progression Modelling](https://mlsanity.com/paper/2508.07032/) (2025)
- [Stretched and measured neural predictions of complex network dynamics](https://mlsanity.com/paper/2301.04900/) (2023)
- [Advanced Global Wildfire Activity Modeling with Hierarchical Graph ODE](https://mlsanity.com/paper/2601.01501/) (2026)

## Abstract (arXiv)

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the structures of high dimensional systems, their elusive continuous-time nonlinear dynamics, and their structural-dynamic dependencies. To address these challenges, we propose to combine Ordinary Differential Equation Systems (ODEs) and Graph Neural Networks (GNNs) to learn continuous-time dynamics on complex networks in a data-driven manner. We model differential equation systems by GNNs. Instead of mapping through a discrete number of neural layers in the forward process, we integrate GNN layers over continuous time numerically, leading to capturing continuous-time dynamics on graphs. Our model can be interpreted as a Continuous-time GNN model or a Graph Neural ODEs model. Our model can be utilized for continuous-time network dynamics prediction, structured sequence prediction (a regularly-sampled case), and node semi-supervised classification tasks (a one-snapshot case) in a unified framework. We validate our model by extensive experiments in the above three scenarios. The promising experimental results demonstrate our model's capability of jointly capturing the structure and dynamics of complex systems in a unified framework.