Navigating the swarm: Deep neural networks command emergent behaviours

Interacting individuals in complex systems often give rise to coherent motion exhibiting coordinated global structures. Such phenomena are ubiquitously observed in nature, from cell migration, bacterial swarms, animal and insect groups, and even human societies. Primary mechanisms responsible for the emergence of collective behavior have been extensively identified, including local alignments based on average or relative velocity, non-local pairwise repulsive-attractive interactions such as distance-based potentials, interplay between local and non-local interactions, and cognitive-based inhomogeneous interactions. However, discovering how to adapt these mechanisms to modulate emergent behaviours remains elusive. Here, we demonstrate that it is possible to generate coordinated structures in collective behavior at desired moments with intended global patterns by fine-tuning an inter-agent interaction rule. Our strategy employs deep neural networks, obeying the laws of dynamics, to find interaction rules that command desired collective structures. The decomposition of interaction rules into distancing and aligning forces, expressed by polynomial series, facilitates the training of neural networks to propose desired interaction models. Presented examples include altering the mean radius and size of clusters in vortical swarms, timing of transitions from random to ordered states, and continuously shifting between typical modes of collective motions. This strategy can even be leveraged to superimpose collective modes, resulting in hitherto unexplored but highly practical hybrid collective patterns, such as protective security formations. Our findings reveal innovative strategies for creating and controlling collective motion, paving the way for new applications in robotic swarm operations, active matter organisation, and for the uncovering of obscure interaction rules in biological systems.