Testing the Distance Duality Relation with Cosmological Observations at high Redshift using Artificial Neural Network

The cosmic Distance Duality Relation (DDR) is a fundamental prediction of metric gravity under photon number conservation. In this work, we perform a model-independent test of the DDR using Pantheon+ type Ia supernovae (SN Ia), \emph{Fermi} gamma-ray bursts (GRBs) with the FULL and GOLD samples, the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) baryon acoustic oscillation (BAO) measurements, and the galaxy-scale strong gravitational lensing (SGL) system samples at high redshift $0.01<z\lesssim 8$ using an artificial neural network (ANN) approach. Our results show that the standard DDR is consistent with cosmological observations at high redshift within the $\sim 2\sigma$ confidence level.