# Neural Ordinary Differential Equation Control of Dynamics on Graphs

arXiv: https://arxiv.org/abs/2006.09773 · HTML: https://mlsanity.com/paper/2006.09773/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2020.

## Built on by (most cited first, 24 of 24)

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- [Community-Aware Temporal Walks: Parameter-Free Representation Learning on Continuous-Time Dynamic Graphs](https://mlsanity.com/paper/2501.11880/) (2025)
- [Control of dynamical systems with neural networks](https://mlsanity.com/paper/2510.12810/) (2025)
- [Power Interpretable Causal ODE Networks: A Unified Model for Explainable Anomaly Detection and Root Cause Analysis in Power Systems](https://mlsanity.com/paper/2602.12592/) (2026)
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## Abstract (arXiv)

We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous time non-linear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs). To do so, we present a neural-ODE control (NODEC) framework and find that it can learn feedback control signals that drive graph dynamical systems into desired target states. While we use loss functions that do not constrain the control energy, our results show, in accordance with related work, that NODEC produces low energy control signals. Finally, we evaluate the performance and versatility of NODEC against well-known feedback controllers and deep reinforcement learning. We use NODEC to generate feedback controls for systems of more than one thousand coupled, non-linear ODEs that represent epidemic processes and coupled oscillators.