Simulations with a "perfect" sample (data set A): results of the NN analysis of a simulated sample of 4,000 objects with a log-flat redshift distribution and a negligible dispersion with respect to a flat ΛCDM model with Ω_M = 0.3. Top panel: Estimated values of I(z) for different values of Ω_M (Eq. 3; the "correct" value for the simulated data is I(z)≡0). Central panel: Hubble diagram with the reconstructed best-fit function obtained from the NN analysis. Bottom panel: Loss values for different values of Ω_M. The minimum is at Ω_M = 0.3, i.e., the "true" value. The corresponding I(z) is consistent with zero at all redshifts. These results demonstrate that the NN analysis is able to recover the correct model and the "true"value of Ω_M.