  In a novel approach employing implicit likelihood inference (ILI), also known
as likelihood-free inference, we calibrate the parameters of cosmological
hydrodynamic simulations against observations, which has previously been
unfeasible due to the high computational cost of these simulations. For
computational efficiency, we train neural networks as emulators on ~1000
cosmological simulations from the CAMELS project to estimate simulated
observables, taking as input the cosmological and astrophysical parameters, and
use these emulators as surrogates to the cosmological simulations. Using the
cosmic star formation rate density (SFRD) and, separately, stellar mass
functions (SMFs) at different redshifts, we perform ILI on selected
cosmological and astrophysical parameters (Omega_m, sigma_8, stellar wind
feedback, and kinetic black hole feedback) and obtain full 6-dimensional
posterior distributions. In the performance test, the ILI from the emulated
SFRD (SMFs) can recover the target observables with a relative error of 0.17%
(0.4%). We find that degeneracies exist between the parameters inferred from
the emulated SFRD, confirmed with new full cosmological simulations. We also
find that the SMFs can break the degeneracy in the SFRD, which indicates that
the SMFs provide complementary constraints for the parameters. Further, we find
that the parameter combination inferred from an observationally-inferred SFRD
reproduces the target observed SFRD very well, whereas, in the case of the
SMFs, the inferred and observed SMFs show significant discrepancies that
indicate potential limitations of the current galaxy formation modeling and
calibration framework, and/or systematic differences and inconsistencies
between observations of the stellar mass function.
