GAlaxy Light profile convolutional neural NETworks (GaLNets). I. fast and accurate structural parameters for billion galaxy samples

Next generation large sky surveys, from ground and space, will observe up to billions of galaxies for which basic structural parameters are needed to study their evolution. This is a challenging task that, for ground-based observations, is complicated by the seeing limited point-spread-function (PSF), strongly affecting the intrinsic light profile of galaxies. To perform fast and accurate analysis of galaxy surface brightness, we have developed a family of "supervised" Convolutional Neural Network (CNN) tools to derive S{\'e}rsic profile parameters of galaxies. In this work, we present the first two Galaxy Light profile convolutional neural Networks (GaLNets) of this family. A first one, trained using galaxy images only (GaLNet-1), and a second one, trained with both galaxy images and the ``local'' PSF (GaLNet-2). The two CNNs have been tested on a subset of public data from the Kilo-Degree Survey (KiDS), as a pathfinder dataset for high-quality ground-based observations. We have compared the results from the two CNNs with structural parameters (namely the total magnitude $mag$, the effective radius $R_{\rm eff}$, and S{\'e}rsic index $n$) derived for the same galaxies by 2DPHOT, as a representative of "standard" PSF-convolved S{\'e}rsic fitting tools. The comparison shows that, provided a suitable prior distribution is adopted, GaLNet-2 can reach an accuracy as high as 2DPHOT, while GaLNet-1 performs slightly worse because it misses the information on the ``local'' PSF. In terms of computational speed, both GaLNets are more than three orders of magnitude faster than standard methods. This first application of CNN to ground-based galaxy surface photometry shows that CNNs are promising tools to perform parametric analyses of very large samples of galaxy light profiles, as expected from surveys like Vera Rubin/LSST, Euclid mission and the Chinese Space Station Telescope.