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In this paper we introduce the \textsc{Deepz} deep learning photometricredshift (photo-$z$) code. As a test case, we apply the code to the PAU survey(PAUS) data in the COSMOS field. \textsc{Deepz} reduces the $\sigma_{68}$scatter statistic by 50\% at $i_{\rm AB}=22.5$ compared to existing algorithms.This improvement is achieved through various methods, including transferlearning from simulations where the training set consists of simulations aswell as observations, which reduces the need for training data. The redshiftprobability distribution is estimated with a mixture density network (MDN),which produces accurate redshift distributions. Our code includes anautoencoder to reduce noise and extract features from the galaxy SEDs. It alsobenefits from combining multiple networks, which lowers the photo-$z$ scatterby 10 percent. Furthermore, training with randomly constructed coadded fluxesadds information about individual exposures, reducing the impact of photometricoutliers. In addition to opening up the route for higher redshift precisionwith narrow bands, these machine learning techniques can also be valuable forbroad-band surveys.

The PAU Survey: Photometric redshifts using transfer learning from simulations