Semi-analytic models are a widely used approach to simulate galaxy properties within a cosmological framework, relying on simplified yet physically motivated prescriptions. They have also proven to be an efficient alternative for generating accurate galaxy catalogs, offering a faster and less computationally expensive option compared to full hydrodynamical simulations. In this paper, we demonstrate that using only galaxy $3$D positions and radial velocities, we can train a graph neural network coupled to a moment neural network to obtain a robust machine learning based model capable of estimating the matter density parameters, $Ω_{\rm m}$, with a precision of approximately 10%. The network is trained on ($25 h^{-1}$Mpc)$^3$ volumes of galaxy catalogs from L-Galaxies and can successfully extrapolate its predictions to other semi-analytic models (GAEA, SC-SAM, and Shark) and, more remarkably, to hydrodynamical simulations (Astrid, SIMBA, IllustrisTNG, and SWIFT-EAGLE). Our results show that the network is robust to variations in astrophysical and subgrid physics, cosmological and astrophysical parameters, and the different halo-profile treatments used across simulations. This suggests that the physical relationships encoded in the phase-space of semi-analytic models are largely independent of their specific physical prescriptions, reinforcing their potential as tools for the generation of realistic mock catalogs for cosmological parameter inference.

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