  Discontinuous Finite Element Methods (DFEM) have been widely used for solving
$S_n$ radiation transport problems in participative and non-participative
media. In the DFEM $S_n$ methodology, the transport equation is discretized
into a set of algebraic equations that have to be solved for each spatial cell
and angular direction, strictly preserving the following of radiation in the
system. At the core of a DFEM solver a small matrix-vector system (of 8
independent equations for tri-linear DFEM in 3D hexehdral cells) has to be
assembled and solved for each cell, angle, energy group, and time step. These
systems are generally solved by direct Gaussian Elimination. The computational
cost of the Gaussian Elimination, repeated for each phase-space cell, amounts
to a large fraction to the total compute time. Here, we have designed a Machine
Learning algorithm based in a shallow Artificial Neural Networks (ANNs) to
replace that Gaussian Elimination step, enabling a sizeable speed up in the
solution process. The key idea is to train an ANN with a large set of solutions
of random one-cell transport problems and then to use the trained ANN to
replace Gaussian Elimination large scale transport solvers. It has been
observed that ANNs decrease the solution times by at least a factor of 4, while
introducing mean absolute errors between 1-3 \% in large scale transport
solutions.
