Neural network reconstructions for the Hubble parameter, growth rate and distance modulus

This paper introduces a new approach to reconstruct cosmological functions using artificial neural networks based on observational measurements with minimal theoretical and statistical assumptions. By networks, we can generate computational models of datasets, then compare them the original ones verify consistency our method. methodology is applicable even small-size datasets. In particular, test proposed method data coming from cosmic chronometers, $f\sigma_8$ measurements, distance modulus Type Ia supernovae. Furthermore, introduce first synthetic covariance matrices through variational autoencoder, systematic matrix supernova compilation.