  A central problem of turbulence theory is to produce a predictive model for
turbulent fluxes. These have profound implications for virtually all aspects of
the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence
produces anomalous fluxes via cross-correlations between fluctuations. In this
work, we introduce a new, data-driven method for parameterizing these fluxes.
The method uses deep supervised learning to infer a reduced mean-field model
from a set of numerical simulations. We apply the method to a simple drift-wave
turbulence system and find a significant new effect which couples the particle
flux to the local \emph{gradient} of vorticity. Notably, here, this effect is
much stronger than the oft-invoked shear suppression effect. We also recover
the result via a simple calculation. The vorticity gradient effect tends to
modulate the density profile. In addition, our method recovers a model for
spontaneous zonal flow generation by negative viscosity, stabilized by
nonlinear and hyperviscous terms. We highlight the important role of symmetry
to implementation of the new method.
