Euclid preparation: XXIII. Derivation of galaxy physical properties with deep machine learning using mock fluxes and H-band images

Next generation telescopes, such as Euclid, Rubin/LSST, and Roman, will open new windows on the Universe, allowing us to infer physical properties for tens of millions of galaxies. Machine learning methods are increasingly becoming the most efficient tools to handle this enormous amount of data, not only as they are faster to apply to data samples than traditional methods, but because they are also often more accurate. Properly understanding their applications and limitations for the exploitation of these data is of utmost importance. In this paper we present an exploration of this topic by investigating how well redshifts, stellar masses, and star-formation rates can be measured with deep learning algorithms for galaxies within data that mimics the Euclid and Rubin/LSST surveys. We find that Deep Learning Neural Networks and Convolutional Neutral Networks (CNN), which are dependent on the parameter space of the sample used for training, perform well in measuring the properties of these galaxies and have an accuracy which is better than traditional methods based on spectral energy distribution fitting. CNNs allow the processing of multi-band magnitudes together with $H_{E}$-band images. We find that the estimates of stellar masses improve with the use of an image, but those of redshift and star-formation rates do not. Our best machine learning results are deriving i) the redshift within a normalised error of less than 0.15 for 99.9% of the galaxies in the sample with S/N>3 in the $H_{E}$-band; ii) the stellar mass within a factor of two ($\sim$0.3 dex) for 99.5% of the considered galaxies; iii) the star-formation rates within a factor of two ($\sim$0.3 dex) for $\sim$70% of the sample. We discuss the implications of our work for application to surveys, mainly but not limited to Euclid and Rubin/LSST, and how measurements of these galaxy parameters can be improved with deep learning.