R² scores of different combinations of training and testing data using the mass column density (upper panel) or velocity dispersion (lower panel) information. 80% of the simulation data were used for training-validation, and 20% was used for the testing in each case located in the diagonal. Left panel: Training and testing data from different MDPL2 redshifts (z = 0, 0.49, 1.03). As expected, for each training set, the R² score is the highest when evaluated on data from the same redshift. Since MDPL2 is a ΛCDM concordance cosmological simulation, the ρ_ta depends on redshift. Therefore, for different redshifts, the model cannot find an apparent correlation between M_vir and R_ta because ρ_ta varies with redshift. The velocity information plot has the same form as the mass, indicating that the model just correlates the mass with the velocity dispersion. Right panel: Training and testing data from different simulations and cosmological models (MDPL2, Virgo ΛCDM, Virgo OCDM, Virgo SCDM, and the merged data from MDPL2 and Virgo ΛCDM). Best models seem to be the ones containing the data from the MDPL2, possibly due to the fact of the larger number of training instances. Negative R² values are a direct consequence of the fact that evaluating a model on another simulation can predict values even worse than the mean (as discussed in Sect. 3), since the target value distribution is an unknown.