# Learning to Swarm with Knowledge-Based Neural Ordinary Differential Equations

arXiv: https://arxiv.org/abs/2109.04927 · HTML: https://mlsanity.com/paper/2109.04927/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2021.

## Built on by (most cited first, 4 of 4)

- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Learning Adaptive Hydrodynamic Models Using Neural ODEs in Complex Conditions](https://mlsanity.com/paper/2410.00490/) (2024)
- [Learning to Identify Graphs from Node Trajectories in Multi-Robot Networks](https://mlsanity.com/paper/2307.04374/) (2023)
- [Knowledge-based Neural Ordinary Differential Equations for Cosserat Rod-based Soft Robots](https://mlsanity.com/paper/2408.07776/) (2024)

## Abstract (arXiv)

Understanding decentralized dynamics from collective behaviors in swarms is crucial for informing robot controller designs in artificial swarms and multiagent robotic systems. However, the complexity in agent-to-agent interactions and the decentralized nature of most swarms pose a significant challenge to the extraction of single-robot control laws from global behavior. In this work, we consider the important task of learning decentralized single-robot controllers based solely on the state observations of a swarm's trajectory. We present a general framework by adopting knowledge-based neural ordinary differential equations (KNODE) -- a hybrid machine learning method capable of combining artificial neural networks with known agent dynamics. Our approach distinguishes itself from most prior works in that we do not require action data for learning. We apply our framework to two different flocking swarms in 2D and 3D respectively, and demonstrate efficient training by leveraging the graphical structure of the swarms' information network. We further show that the learnt single-robot controllers can not only reproduce flocking behavior in the original swarm but also scale to swarms with more robots.