  We explore the potential of an artificial neural network (ANN) based method
intelligence to probe the propagation of cosmic $\gamma$-ray photons in the
extragalactic Universe. The journey of $\gamma$-rays emitted from a distant
source like blazar to the observer at the Earth is impeded by the absorption
through the interaction with the extragalactic background light (EBL), leading
to an electron-positron pair production. This process dominates for gamma ray
photons with energy above 10 GeV propagating over the cosmological distances.
The effect of $\gamma$-ray attenuation is characterized by a physical quantity
called \emph{optical depth}, which strongly depends on the $\gamma$-ray photon
energy, redshift of the source, and density of the EBL photons. We estimate the
optical depth values for $\gamma$-ray energies above 10 GeV emitted from the
sources at redshifts in the range 0.01 to 1 using three different and most
promising EBL models. These optical depth estimates are randomly divided into
two data sets for training and testing of the ANN using energy, redshift as
inputs and optical depth as output. The optimization of ANN-performance for
each EBL model employs standard back-propagation (BP) and radial-basis function
(RBF) algorithms. The performance of the ANN model using the RBF is found to be
superior to the BP method. In particular, the RBF-ANN with 40 neurons in the
hidden layer corresponding to the EBL model proposed by Finke et al. (2010)
shows the best performance for the propagation of $\gamma$-rays in the
Universe.
