  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, and a Taylor-Green vortex 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 based on a conventional autoencoder where
compression is performed in a continuous space, our model improves the CR by
more than $30$ percent, and reduces the MSE by an order of magnitude. Our
compression model is an attractive solution for situations where fast, high
quality and low-overhead encoding and decoding of large data are required.
