Commanding emergent behavior with neural networks

<h2>Summary</h2> Interacting individuals in complex systems often give rise to collective motions, exhibiting coherent and coordinated global structures. Despite extensive studies on collective motions, controlling such emergent behaviors remains elusive. Here, we demonstrate a strategy to control collective motions at desired moments with intended global patterns. This strategy employs deep neural networks that obey the laws of dynamics to find inter-agent interaction rules that produce desired collective structures. Examples presented include adjusting the average radius and cluster size in vortical swarms, timing transitions from random to ordered states, and inducing collective modes within obstacles and confined areas. Furthermore, the strategy can be extended to analyze real-world data, reproducing collective patterns in bird flocks. These findings provide a pathway for navigating robot swarms, organizing active matter, and uncovering hidden rules in biological flocks under the guidance of deep neural networks.