Robust field-level inference with dark matter halos

We train graph neural networks on halo catalogues from Gadget N-body simulations to perform field-level likelihood-free inference of cosmological parameters. The catalogues contain lesssim5,000 halos with masses gtrsim 1010~h-1M_odot in a periodic volume of (25~h-1rm Mpc)3; every halo in the catalogue 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 Omegarm m and σ8 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 Omegarm m and σ8 when tested using halo catalogues from thousands of N-body simulations run with five different N-body codes: Abacus, CUBEP3M, Enzo, PKDGrav3, and Ramses. Surprisingly, the model trained to infer Omegarm 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.