A Non-parametric Reconstruction of the Hubble Parameter $H(z)$ Based on Radial Basis Function Neural Networks

Abstract: Accurately measuring the Hubble parameter is vital for understanding the expansion history and properties of the universe. In this paper, we propose a new method that supplements the covariance between redshift pairs to improve the reconstruction of the Hubble parameter using the OHD dataset. Our approach utilizes a cosmological model-independent radial basis function neural network (RBFNN) to describe the Hubble parameter as a function of redshift effectively. Our experiments show that this method results in a reconstructed Hubble parameter of $H_0 = 67.1\pm9.7~\mathrm{km~s^{-1}~Mpc^{-1}}$ , which is more noise-resistant and fits better with the $\Lambda$CDM model at high redshifts. Providing the covariance between redshift pairs in subsequent observations will significantly improve the reliability and accuracy of Hubble parametric data reconstruction. Future applications of this method could help overcome the limitations of previous methods and lead to new advances in our understanding of the universe.