Gamma-Ray Bursts Calibrated from the Observational $H(z)$ Data in Artificial Neural Network Framework
In this paper, we calibrate the luminosity relation of gamma-ray bursts (GRBs) from an Artificial Neural Network (ANN) framework for reconstructing the Hubble parameter \unboldmath{$H(z)$} from the latest observational Hubble data (OHD) obtained with the cosmic chronometers method in a cosmology-independent way. We consider the physical relationships between the data to introduce the covariance matrix and KL divergence of the data into the loss function and calibrate the Amati relation ($E_{\rm p}$--$E_{\rm iso}$) by selecting the optimal ANN model with the A219 sample and the J220 sample at low redshift. Combining the Pantheon+ type Ia supernovae (SNe Ia) sample and Baryon acoustic oscillations (BAOs) from Dark Energy Spectroscopy Instrument (DESI) with GRBs at high redshift in the Hubble diagram by Markov Chain Monte Carlo numerical method, we find that the $Λ$CDM model is preferred over the $w$CDM and CPL models with joint constraints by the Akaike Information Criterion and Bayesian Information Criterion.