Left panel: Stellar mass functions at z = 0.0, 1.5, 3.0 using the Leja et al. (2020) continuity model in dotted, solid, and dashed lines respectively. The model parameters and their uncertainties are taken from the same literature. We take the median model (SMF50, red lines) and models at 68% confidence level, where SMF84 (green lines) denotes the upper limit and SMF16 (blue lines) denotes the lower limit. Middle panel: Corresponding histograms of galaxy magnitude for different population models. Right panel: Three test sets of simulations are generated using the models. The blue line with error bars presents the ensemble-averaged R measured in the three sets, while the orange line shows the emulator predictions. The emulator is trained on a training set of SMF50 only.