  We train graph neural networks to perform field-level likelihood-free
inference using galaxy catalogs from state-of-the-art hydrodynamic simulations
of the CAMELS project. Our models are rotational, translational, and
permutation invariant and do not impose any cut on scale. From galaxy catalogs
that only contain $3$D positions and radial velocities of $\sim 1, 000$
galaxies in tiny $(25~h^{-1}{\rm Mpc})^3$ volumes our models can infer the
value of $\Omega_{\rm m}$ with approximately $12$ % precision. More
importantly, by testing the models on galaxy catalogs from thousands of
hydrodynamic simulations, each having a different efficiency of supernova and
AGN feedback, run with five different codes and subgrid models - IllustrisTNG,
SIMBA, Astrid, Magneticum, SWIFT-EAGLE -, we find that our models are robust to
changes in astrophysics, subgrid physics, and subhalo/galaxy finder.
Furthermore, we test our models on $1,024$ simulations that cover a vast region
in parameter space - variations in $5$ cosmological and $23$ astrophysical
parameters - finding that the model extrapolates really well. Our results
indicate that the key to building a robust model is the use of both galaxy
positions and velocities, suggesting that the network have likely learned an
underlying physical relation that does not depend on galaxy formation and is
valid on scales larger than $\sim10~h^{-1}{\rm kpc}$.
