Collective adaptation to time-dependent targets for active Brownian particles
Abstract
We consider a minimal model of active agents which collectively learn to reach a target macroscopic state via a decentralized adaptation process. Agents are modeled as active Brownian particles which randomly reorient to a given direction through tumbling events. An average target state is encoded into a reward function evaluated by each agent. Agents can tune one of the parameters of their microscopic dynamics, called `policy' (e.g., speed or reorientation direction), to optimize their reward function thanks to information exchange with neighboring agents. We describe the evolution of the policy distribution across the agent population with a kinetic theory, under the assumption that the adaptation process is slow with respect to the physical dynamics. The adaptation process is illustrated on several learning protocols with either fixed or time-dependent target velocities. A characteristic learning time τ combining teaching and mutations emerges from the dynamics. For time-oscillating targets at angular frequency ω, the collective dynamics oscillates in time, with an oscillation amplitude and phase shift determined by the product ωτ. An unlocking transition to a non-adaptable state is also observed for a rotating target velocity.
Related
- Collective Behavior of Intelligent Active Brownian Particles in the Presence of a Static Obstacle
- Stationary distribution of active Brownian particles in a bounded domain
- Diffusion of chiral active Brownian particles in oscillatory Poiseuille flow
- Static and dynamic density correlations of interacting active Brownian particles
- Microscopic dynamics of contagion using active Brownian particles: universal scaling and propagation controlled by protection
BibTeX
@misc{jung2026collective,
title = {{Collective adaptation to time-dependent targets for active Brownian particles}},
author = {Gerhard Jung and Eric Bertin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15839},
eprint = {2609.15839},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15839},
}
RIS
TY - UNPB
TI - Collective adaptation to time-dependent targets for active Brownian particles
AU - Gerhard Jung
AU - Eric Bertin
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15839
UR - https://arxiv.org/abs/2609.15839
AB - We consider a minimal model of active agents which collectively learn to reach a target macroscopic state via a decentralized adaptation process. Agents are modeled as active Brownian particles which randomly reorient to a given direction through tumbling events. An average target state is encoded into a reward function evaluated by each agent. Agents can tune one of the parameters of their microscopic dynamics, called `policy' (e.g., speed or reorientation direction), to optimize their reward function thanks to information exchange with neighboring agents. We describe the evolution of the policy distribution across the agent population with a kinetic theory, under the assumption that the adaptation process is slow with respect to the physical dynamics. The adaptation process is illustrated on several learning protocols with either fixed or time-dependent target velocities. A characteristic learning time τ combining teaching and mutations emerges from the dynamics. For time-oscillating targets at angular frequency ω, the collective dynamics oscillates in time, with an oscillation amplitude and phase shift determined by the product ωτ. An unlocking transition to a non-adaptable state is also observed for a rotating target velocity.
ER -