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Reconstructing Functions and Estimating Parameters with Artificial Neural Networks: A Test with the Hubble Parameter and SNe Ia
Guo-Jian Wang, Xiao-Jiao Ma, Si-Yao Li, Jun-Qing Xia
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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.
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