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Turbulence plays a key role in star formation in molecular clouds, affectingstar cluster primordial properties. As modelling present-day objects hinges onour understanding of their initial conditions, better constraints on turbulencecan result in windfalls in Galactic archaeology, star cluster dynamics and starformation. Observationally, constraining the spectral index of turbulent gasusually involves computing spectra from velocity maps. Here we suggest thatinformation on the spectral index might be directly inferred from columndensity maps (possibly obtained by dust emission/absorption) through deeplearning. We generate mock density maps from a large set of adaptive meshrefinement turbulent gas simulations using the hydro-simulation code RAMSES. Wetrain a convolutional neural network (CNN) on the resulting images to predictthe turbulence index, optimize hyper-parameters in validation and test on aholdout set. Our adopted CNN model achieves a mean squared error of 0.024 inits predictions on our holdout set, over underlying spectral indexes rangingfrom 3 to 4.5. We also perform robustness tests by applying our model toaltered holdout set images, and to images obtained by running simulations atdifferent resolutions. This preliminary result on simulated density mapsencourages further developments on real data, where observational biases andother issues need to be taken into account.

Measuring the spectral index of turbulent gas with deep learning from projected density maps