Euclid preparation. XIII. Forecasts for galaxy morphology with the Euclid Survey using deep generative models ; Euclid preparation. XIII. Forecasts for galaxy morphology with the Euclid Survey using deep generative models: XIII. Forecasts for galaxy morphology with the Euclid Survey using deep generative models

International audience ; We present a machine learning framework to simulate realistic galaxies for the Euclid Survey, producing more complex and realistic galaxies than the analytical simulations currently used in Euclid. The proposed method combines a control on galaxy shape parameters offered by analytic models with realistic surface brightness distributions learned from real Hubble Space Telescope observations by deep generative models. We simulate a galaxy field of $0.4\,\rm{deg}^2$ as it will be seen by the Euclid visible imager VIS, and we show that galaxy structural parameters are recovered to an accuracy similar to that for pure analytic Sérsic profiles. Based on these simulations, we estimate that the Euclid Wide Survey (EWS) will be able to resolve the internal morphological structure of galaxies down to a surface brightness of $22.5\,\rm{mag}\,\rm{arcsec}^{-2}$, and the Euclid Deep Survey (EDS) down to $24.9\,\rm{mag}\,\rm{arcsec}^{-2}$. This corresponds to approximately $250$ million galaxies at the end of the mission and a $50\,\%$ complete sample for stellar masses above $10^{10.6}\,\rm{M}_\odot$ (resp. $10^{9.6}\,\rm{M}_\odot$) at a redshift $z\sim0.5$ for the EWS (resp. EDS). The approach presented in this work can contribute to improving the preparation of future high-precision cosmological imaging surveys by allowing simulations to incorporate more realistic galaxies.