Reconstructing Functions and Estimating Parameters with Artificial
  Neural Networks: A Test with the Hubble Parameter and SNe Ia
  In this work, we propose a new nonparametric approach for reconstructing a
function from observational data using an Artificial Neural Network (ANN),
which has no assumptions about the data and is a completely data-driven
approach. We test the ANN method by reconstructing functions of the Hubble
parameter measurements $H(z)$ and the distance-redshift relation $D_L(z)$ of
Type Ia supernovae. We find that both $H(z)$ and $D_L(z)$ can be reconstructed
with high accuracy. Furthermore, we estimate cosmological parameters using the
reconstructed functions of $H(z)$ and $D_L(z)$ and find the results are
consistent with those obtained using the observational data directly.
Therefore, we propose that the function reconstructed by ANN can represent the
actual distribution of observational data and can be used for parameter
estimation in further cosmological research. In addition, we present a new
strategy for training and evaluating the neural network, and a code for
reconstructing functions using ANN has been developed and is available for
download.
