Using artificial neural networks to accelerate transport solves

Discontinuous Finite Element Methods (DFEM) have been widely used for solving S_N radiation transport problems in participative and non-participative media. In this method, small matrix-vector systems are assembled and solved for each cell, angle, energy group, and time step while sweeping through the computational mesh. In practice, these systems are generally solved directly using Gaussian elimination, as computational acceleration for solving this small systems are often inadequate. Nonetheless, the computational cost of assembling and solving these local systems, repeated for each cell in the phase-space, can amount to a large fraction of the total computing time. In this paper, a Machine Learning algorithm is designed to accelerate the solution of local systems. This one is based on Artificial Neural Networks (ANNs). Its key idea is training an ANN with a large set of solutions to random one-cell transport problems and, then, replacing the assembling and solution of the local systems by the feedforward evaluation of the trained ANN. It is observed that the optimized ANNs are able to reduce the compute times by a factor of ∼ 3.6 per source iteration, while introducing mean absolute errors between 0.5 − 2% in transport solutions.