In this thesis, we expand the scope of a previously introduced Artificial Neural Network (ANN) method to solve the slab-geometry discrete ordinates (S$_N$) neutron transport equations. Specifically, we extend the method to energy-dependent (multi-group) fixed source problems involving heterogeneous media and more general boundary conditions - vacuum and incident flux conditions. Comparisons of the results obtained by this method for the Kornreich & Parsons problem and the Reed problem (1-group) with the results obtained from traditional discrete ordinates solutions with the linear discontinuous finite element spatial discretization. We also consider a comparison of the results obtained for the De-Barros problem (2-group) by the ANN method with the results obtained from the LDFEM discretization of the S$_N$ equations. Generalization of the ANN method to the multi-group slab-geometry discrete ordinate equation in a heterogeneous medium with isotropic scattering is presented. We also explore the effects of various neural network architecture parameters, namely the number of nodes, number of hidden layers, and activation function modifications, on the performance of the ANN method for these problems.