Sweep-Net: An Artificial Neural Network for radiation transport solves

Abstract

Discontinuous Galerkin Finite Element Methods (DGFEM) have been widely used for solving SN radiation transport problems in participative and non-participative media. Global matrices are not assembled when sweeping through the computational domain, but only small matrix-vector systems are assembled and solved for each cell, angle, energy group, and time step (e.g., systems with 8 independent equations for tri-linear DGFEM in 3D hexahedral cells). These systems are generally solved directly using Gaussian elimination. 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 computation time. Therefore, a Machine Learning algorithm is designed in this paper, based on Artificial Neural Networks (ANNs), to replace the assembling and solution of the local systems, enabling a sizable speed up in the solution process. The key idea is to train an ANN with a large set of solutions to random one-cell transport problems and, then, replace the assembling and solution of the local systems by the feedforward evaluation of the trained ANN in large-scale transport solvers. These ANNs are optimized to reproduce the solutions obtained in radiation transport solves, while minimizing the number of operations involved in its feedforward evaluation. 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.