How do swarm robots learn to organize themselves in stages?

Coordinating hundreds of robots without central control is hard, especially when behavior must change in stages. PhySwarm combines macroscopic physics (advection-diffusion-reaction equations) with microscopic robot motion, using reinforcement learning to train a neural controller that maps local observations to physical parameters. Tested on foraging, formation changes, and search-and-rescue, the system generates interpretable multi-stage behaviors and reveals which physics mechanisms (diffusion, transport, phase transitions) drive swarm organization.