Gamma-Ray Bursts Calibrated by Using Artificial Neural Networks from the Pantheon+ Sample

In this paper, we calibrate the luminosity relation of gamma-ray bursts (GRBs) by Artificial Neural Networks (ANN) which is employed to analyze the Pantheon+ sample of type Ia supernovae (SNe Ia) in a manner independent of cosmological assumptions. The A219 GRB dataset are used to calibrate the Amati relation ($E_{\mathrm{p}}$-$E_{\mathrm{i}\mathrm{s}\mathrm{o}}$) at low redshift with the ANN framework, facilitating the construction of the Hubble diagram at higher redshifts. Cosmological models are constrained with GRBs at high-redshift and the latest observational Hubble data (OHD) via a Markov Chain Monte Carlo numerical approach. For the Chevallier-Polarski-Linder (CPL) model within a flat universe, we obtain ${\mathrm{\Omega }}_{\mathrm{m}}=0.321_{-0.069}^{+0.078}$, $h=0.654_{-0.071}^{+0.053}$, $w_0=-1.02_{-0.50}^{+0.67}$, and $w_a=-0.98_{-0.58}^{+0.58}$ at the 1-$\sigma$ confidence level, which indicating a preference for dark energy with potential redshift evolution ($w_a\mathrm{\ne }0$). These findings by using ANN align closely with those derived from GRBs calibrated by using Gaussian Processes.