Solving the Discretised Boltzmann Transport Equations using Neural Networks: Applications in Neutron Transport

Abstract: In this paper we solve the Boltzmann transport equation using AI libraries. The reason why this is attractive is because it enables one to use the highly optimised software within AI libraries, enabling one to run on different computer architectures and enables one to tap into the vast quantity of community based software that has been developed for AI and ML applications e.g. mixed arithmetic precision or model parallelism. Here we take the first steps towards developing this approach for the Boltzmann transport equation and develop the necessary methods in order to do that effectively. This includes: 1) A space-angle multigrid solution method that can extract the level of parallelism necessary to run efficiently on GPUs or new AI computers. 2) A new Convolutional Finite Element Method (ConvFEM) that greatly simplifies the implementation of high order finite elements (quadratic to quintic, say). 3) A new non-linear Petrov-Galerkin method that introduces dissipation anisotropically.