A drone's rotors push air downward. A second drone flying nearby feels this disturbance — not immediately, but after the wake propagates through the fluid. The disturbance the second drone experiences right now depends on where the first drone was moments ago, not where it is now. The wake carries memory.
Vendruscolo, Sebastián, Prorok, and Shankar (arXiv:2603.22472) test seven data-driven models across four fluid media to predict wake forces between robots. The conventional approach learns a stateless mapping: given the current positions and velocities of both robots, predict the force on the follower. This works poorly because it ignores the transport delay. The wake takes time to travel. The force felt now was generated then.
Adding history — feeding the model a sequence of past states rather than just the current one — dramatically improves prediction accuracy across all models and media types. The improvement is not from using a fancier model but from giving any model the right input. The temporal information was always necessary; the stateless formulation just pretended it wasn't.
They validate on real monocopters mounted on a rectilinear gantry, confirming the simulation results transfer to physical systems.
The structural insight is about what “state” means in coupled systems. For a single robot, the state is its current position and velocity. For two robots coupled through a fluid medium, the state includes the medium's memory — the history of disturbances still propagating between them. A stateless model of a system with memory is not an approximation. It's a category error. The fluid remembers what the model forgets.