  Turbulence plays a key role in star formation in molecular clouds, affecting
star cluster primordial properties. As modelling present-day objects hinges on
our understanding of their initial conditions, better constraints on turbulence
can result in windfalls in Galactic archaeology, star cluster dynamics and star
formation. Observationally, constraining the spectral index of turbulent gas
usually involves computing spectra from velocity maps. Here we suggest that
information on the spectral index might be directly inferred from column
density maps (possibly obtained by dust emission/absorption) through deep
learning. We generate mock density maps from a large set of adaptive mesh
refinement turbulent gas simulations using the hydro-simulation code RAMSES. We
train a convolutional neural network (CNN) on the resulting images to predict
the turbulence index, optimize hyper-parameters in validation and test on a
holdout set. Our adopted CNN model achieves a mean squared error of 0.024 in
its predictions on our holdout set, over underlying spectral indexes ranging
from 3 to 4.5. We also perform robustness tests by applying our model to
altered holdout set images, and to images obtained by running simulations at
different resolutions. This preliminary result on simulated density maps
encourages further developments on real data, where observational biases and
other issues need to be taken into account.
