The Euclid mission is generating a vast amount of imaging data in four broadband filters at a high angular resolution. This data will allow for the detailed study of mass, metallicity, and stellar populations across galaxies that will constrain their formation and evolutionary pathways. Transforming the Euclid imaging for large samples of galaxies into maps of physical parameters in an efficient and reliable manner is an outstanding challenge. Here, we investigate the power and reliability of machine learning techniques to extract the distribution of physical parameters within well-resolved galaxies. We focus on estimating stellar mass surface density, mass-averaged stellar metallicity, and age. We generated noise-free synthetic high-resolution (100 pc × 100 pc) imaging data in the Euclid photometric bands for a set of 1154 galaxies from the TNG50 cosmological simulation. The images were generated with the SKIRT radiative transfer code, taking into account the complex 3D distribution of stellar populations and interstellar dust attenuation. We used a machine learning framework to map the idealised mock observational data to the physical parameters on a pixel-by-pixel basis. We find that stellar mass surface density can be accurately recovered with a ≤0.130 dex scatter. Conversely, stellar metallicity and age estimates are, as expected, less robust, but they still contain significant information that originates from underlying correlations at a sub-kiloparsec scales between stellar mass surface density and stellar population properties. As a corollary, we show that TNG50 follows a spatially resolved mass-metallicity relation that is consistent with observations. Due to its relatively low computational and time requirements, which has a time-frame of minutes without dedicated high performance computing infrastructure once it has been trained, our method allows for fast and robust estimates of the stellar mass surface density distributions of nearby galaxies from four-filter Euclid imaging data. Equivalent estimates of stellar population properties (stellar metallicity and age) are less robust but still hold value as first-order approximations across large samples.
