Reconstructing Functions and Estimating Parameters with Artificial Neural Networks: A Test with the Hubble Parameter and SNe Ia

TL;DR

This paper introduces a nonparametric neural network-based method for reconstructing cosmological functions from observational data, demonstrating high accuracy and consistent parameter estimation, with a new training strategy and available code.

Contribution

It presents a novel ANN-based approach for reconstructing cosmological functions without assumptions, including a new training strategy and publicly available code.

Findings

High-accuracy reconstruction of $H(z)$ and $D_L(z)$ functions

Consistent cosmological parameter estimation with reconstructed functions

A new neural network training and evaluation strategy

Abstract

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.