  The predictive capabilities of turbulent flow simulations, critical for
aerodynamic design and weather prediction, hinge on the choice of turbulence
models. The abundance of data from experiments and simulations and the advent
of machine learning have provided a boost to turbulence modeling efforts.
However, simulations of turbulent flows remain hindered by the inability of
heuristics and supervised learning to model the near-wall dynamics. We address
this challenge by introducing scientific multi-agent reinforcement learning
(SciMARL) for the discovery of wall models for large-eddy simulations (LES). In
SciMARL, discretization points act also as cooperating agents that learn to
supply the LES closure model. The agents self-learn using limited data and
generalize to extreme Reynolds numbers and previously unseen geometries. The
present simulations reduce by several orders of magnitude the computational
cost over fully-resolved simulations while reproducing key flow quantities. We
believe that SciMARL creates unprecedented capabilities for the simulation of
turbulent flows.
