A hierarchical reduced-order model applied to nuclear reactors

Abstract

Modelling the neutron transport of a nuclear reactor is a very computationally demanding task that requires a large number of degrees of freedom to accurately capture all of the physics. For a complete reactor picture, other physics must be incorporated, through coupling, further exacerbating the computational demand. Computational modelling has many benefits: optimisation, real-time analysis, and safety analysis are some of the more important ones. However, nuclear modelling has yet to capitalise on these, and existing approaches are too computationally demanding. Machine Learning has seen incredible growth over the last decade, but it has yet to be utilised within the nuclear modelling community to the same extent. The frameworks available represent incredibly efficient and optimised code, having been written to run on GPUs and AI computers. Presented here is a physics-driven neural network that solves neutron transport, first for the diffusion approximation and then extended to the whole transport problem. One method that can potentially reduce the computational complexity is Reduced-Order Modelling (ROM), which is a way to define a low-dimensional space in which a high-dimensional system can be approximated. These established methods can be used with machine learning methods, potentially reducing computational costs further than either method individually. A method to utilise autoencoders with a projection-based framework is also presented here. The structure of a reactor can be broken down, forming a hierarchy which starts with the reactor core, which is populated by fuel assemblies, which are then populated by fuel rods. This hierarchy means that materials are repeated within a solution, and many existing methods do not capitalise on this and instead resolve the entire global domain. This research presents two ways to utilise this structure with ROM. The first involves combining it with domain decomposition, producing ROMs for the sub-structures. The second presents a hierarchical interpolating method, reducing the number of sub-domains within the solution that need to be resolved.