Reconstructing the Hubble diagram of gamma-ray bursts using deep learning

We calibrate the distance and reconstruct Hubble diagram of gamma-ray bursts (GRBs) using deep learning. construct an artificial neural network, which combines recurrent network Bayesian train Pantheon compilation type-Ia supernovae. The trained is used to 174 GRBs based on Combo-relation. verify that there no evident redshift evolution Combo-relation, obtain slope intercept parameters, $\gamma=0.856^{+0.083}_{-0.078}$ $\log A=49.661^{+0.199}_{-0.217}$, with intrinsic scatter $\sigma_{\rm int}=0.228^{+0.041}_{-0.040}$. Our calibrating method independent cosmological model, thus calibrated can be directly constrain parameters. It shown alone tightly $\Lambda$CDM $\Omega_{\rm M}=0.280^{+0.049}_{-0.057}$. However, constraint $\omega$CDM model relatively looser, M}=0.345^{+0.059}_{-0.060}$ $\omega<-1.414$. combination M}=0.336^{+0.055}_{-0.050}$ $\omega=-1.141^{+0.156}_{-0.135}$.