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Abstract We train graph neural networks on halo catalogs from Gadget N -body simulations to perform field-level likelihood-free inference of cosmological parameters. The catalogs contain ≲5000 halos with masses ≳10 10 h −1 M ⊙ in a periodic volume of ( 25 h − 1 Mpc ) 3 ; every halo in the catalog is characterized by several properties such as position, mass, velocity, concentration, and maximum circular velocity. Our models, built to be permutationally, translationally, and rotationally invariant, do not impose a minimum scale on which to extract information and are able to infer the values of Ω m and σ 8 with a mean relative error of ∼6%, when using positions plus velocities and positions plus masses, respectively. More importantly, we find that our models are very robust: they can infer the value of Ω m and σ 8 when tested using halo catalogs from thousands of N -body simulations run with five different N -body codes: Abacus, CUBEP 3 M, Enzo, PKDGrav3, and Ramses. Surprisingly, the model trained to infer Ω m also works when tested on thousands of state-of-the-art CAMELS hydrodynamic simulations run with four different codes and subgrid physics implementations. Using halo properties such as concentration and maximum circular velocity allow our models to extract more information, at the expense of breaking the robustness of the models. This may happen because the different N -body codes are not converged on the relevant scales corresponding to these parameters.