  Inference problems for two-dimensional snapshots of rotating turbulent flows
are studied. We perform a systematic quantitative benchmark of point-wise and
statistical reconstruction capabilities of the linear Extended Proper
Orthogonal Decomposition (EPOD) method, a non-linear Convolutional Neural
Network (CNN) and a Generative Adversarial Network (GAN). We attack the
important task of inferring one velocity component out of the measurement of a
second one, and two cases are studied: (I) both components lay in the plane
orthogonal to the rotation axis and (II) one of the two is parallel to the
rotation axis. We show that EPOD method works well only for the former case
where both components are strongly correlated, while CNN and GAN always
outperform EPOD both concerning point-wise and statistical reconstructions. For
case (II), when the input and output data are weakly correlated, all methods
fail to reconstruct faithfully the point-wise information. In this case, only
GAN is able to reconstruct the field in a statistical sense. The analysis is
performed using both standard validation tools based on $L_2$ spatial distance
between the prediction and the ground truth and more sophisticated multi-scale
analysis using wavelet decomposition. Statistical validation is based on
standard Jensen-Shannon divergence between the probability density functions,
spectral properties and multi-scale flatness.
