Constraining the polarisation flux density and angle of point sources by training a convolutional neural network

Constraining the polarisation properties of extragalactic point sources is a relevant task not only because they are one of the main contaminants for primordial cosmic microwave background B-mode detection if the tensor-to-scalar ratio is lower than r = 0.001, but also for a better understanding of the properties of radio-loud active galactic nuclei. We develop and train a machine learning model based on a convolutional neural network to learn how to estimate the polarisation flux density and angle of point sources embedded in cosmic microwave background images knowing only their positions. To train the neural network, we use realistic simulations of patches of area 32x32 pixels at the 217 GHz Planck channel with injected point sources at their centres. The patches also contain a realistic background composed by dust, the CMB and instrumental noise. Firstly, we study the comparison between true and estimated polarisation flux densities for P, Q and U. Secondly, we analyse the comparison between true and estimated polarisation angles. Finally, we study the performance of our model with real data and we compare our results against the PCCS2. We obtain that our model is reliable to constrain the polarisation flux above 80 mJy. For this limit, we obtain errors lower than 30%. Training the same network with Q and U, the reliability limit is above +-250 mJy for determining the polarisation angle of both Q and U sources with a 1sigma uncertainty of +-29deg and +-32deg for Q and U sources respectively. We obtain similar results to the PCCS2 for some sources, although we also find discrepancies in the 300-400 mJy flux density range with respect to the Planck catalogue. Based on these results, our model seems to be a promising tool to give estimations of the polarisation flux densities and angles of point sources above 80 mJy in any catalogue with practically null computational time.