Machine-learning cosmological inferences from X-ray galaxy-cluster survey catalogs

Galaxy clusters provide critical constraints on cosmological parameters; however, traditional approaches based on mass–observable scaling relations are subject to systematic uncertainties. Here, we present a machine-learning framework that directly infers cosmological parameters from real eROSITA galaxy cluster observations, bypassing explicit mass calibration. We train a random forest algorithm on Magneticum multi-cosmology hydrodynamical simulations and apply it to observed X-ray properties (gas luminosity, mass, and temperature) at different redshifts from the eROSITA catalogs. This method yields cosmological constraints including the matter density Ωm=0.30^+0.03_-0.02, and the 8 Mpc/h fluctuation amplitude, σ8=0.81^+0.01_-0.01, consistent with current state-of-the-art probes. Unlike other low-redshift cosmological datasets, these parameters show no significant tension with Cosmic Microwave Background inferences from the Planck mission. In contrast, our inference of the Hubble constant, h0=0.710^+0.004_-0.004, shows a significant deviation from the Planck value and lies slightly below most late–Universe determinations, while remaining comfortably consistent with the Tip of the Red Giant Branch (\textit{TRGB}) measurements. This suggests a potential reduction of the early–late Universe Hubble tension. This study represents the first direct cosmological inference from observational cluster data using machine learning trained on multi-cosmology simulations. It establishes an alternative route to precision cosmology using galaxy cluster observations via machine learning, and highlights the potential of large-scale X-ray surveys to deliver independent tests of the standard cosmological model.