  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.
