  Numerical simulations of turbulent flows are well known to pose extreme
computational challenges due to the huge number of dynamical degrees of freedom
required to correctly describe the complex multi-scale statistical correlations
of the velocity. On the other hand, kinetic mesoscale approaches based on the
Boltzmann equation, have the potential to describe a broad range of flows,
stretching well beyond the special case of gases close to equilibrium, which
results in the ordinary Navier-Stokes dynamics. Here we demonstrate that, by
properly tuning, a kinetic approach can statistically reproduce the
quantitative dynamics of the larger scales in turbulence, thereby providing an
alternative, computationally efficient and physically rooted approach towards
subgrid scale (SGS) modeling in turbulence. More specifically we show that by
leveraging on data from fully resolved Direct Numerical Simulation (DNS) data
we can learn a collision operator for the discretized Boltzmann equation solver
(the lattice Boltzmann method), which effectively implies a turbulence subgrid
closure model. The mesoscopic nature of our formulation makes the learning
problem fully local in both space and time, leading to reduced computational
costs and enhanced generalization capabilities. We show that the model offers
superior performance compared to traditional methods, such as the Smagorinsky
model, being less dissipative and, therefore, being able to more closely
capture the intermittency of higher-order velocity correlations.
