  Inferring the values and uncertainties of cosmological parameters in a
cosmology model is of paramount importance for modern cosmic observations. In
this paper, we use the simulation-based inference (SBI) approach to estimate
cosmological constraints from a simplified galaxy cluster observation analysis.
Using data generated from the Quijote simulation suite and analytical models,
we train a machine learning algorithm to learn the probability function between
cosmological parameters and the possible galaxy cluster observables. The
posterior distribution of the cosmological parameters at a given observation is
then obtained by sampling the predictions from the trained algorithm. Our
results show that the SBI method can successfully recover the truth values of
the cosmological parameters within the 2{\sigma} limit for this simplified
galaxy cluster analysis, and acquires similar posterior constraints obtained
with a likelihood-based Markov Chain Monte Carlo method, the current state-of
the-art method used in similar cosmological studies.
