  Analyzing large-scale data from simulations of turbulent flows is memory
intensive, requiring significant resources. This major challenge highlights the
need for data compression techniques. In this study, we apply a
physics-informed Deep Learning technique based on vector quantization to
generate a discrete, low-dimensional representation of data from simulations of
three-dimensional turbulent flows. The deep learning framework is composed of
convolutional layers and incorporates physical constraints on the flow, such as
preserving incompressibility and global statistical characteristics of the
velocity gradients. The accuracy of the model is assessed using statistical,
comparison-based similarity and physics-based metrics. The training data set is
produced from Direct Numerical Simulation of an incompressible, statistically
stationary, isotropic turbulent flow.
  The performance of this lossy data compression scheme is evaluated not only
with unseen data from the stationary, isotropic turbulent flow, but also with
data from decaying isotropic turbulence, a Taylor-Green vortex flow, and a
turbulent channel flow. Defining the compression ratio (CR) as the ratio of
original data size to the compressed one, the results show that our model based
on vector quantization can offer CR$=85$ with a mean square error (MSE) of
$O(10^{-3})$, and predictions that faithfully reproduce the statistics of the
flow, except at the very smallest scales where there is some loss. Compared to
the recent study of Glaws. et. al. (Physical Review Fluids, 5(11):114602,
2020), which was based on a conventional autoencoder (where compression is
performed in a continuous space), our model improves the CR by more than $30$
percent...
