Reduced-Order Modelling with Domain Decomposition Applied to Multi-Group Neutron Transport

Abstract

Solving the neutron transport equations is a demanding computational challenge. This paper combines reduced-order modelling with domain decomposition to develop an approach that can tackle such problems. The idea is to decompose the domain of a reactor, form basis functions locally in each sub-domain and construct a reduced-order model from this. Several different ways of constructing the basis functions for local sub-domains are proposed, and a comparison is given with a reduced-order model that is formed globally. A relatively simple one-dimensional slab reactor provides a test case with which to investigate the capabilities of the proposed methods. The results show that domain decomposition reduced-order model methods perform comparably with the global reduced-order model when the total number of reduced variables in the system is the same with the potential for the offline computational cost to be significantly less expensive.

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

“…Neural networks have been used to obtain closures for P N -type systems of moment equations of the BTE [62,63]. Data-driven ROMs have also been created for particle transport problems in nuclear reactor-physics applications [64,65,66,67], including (i) pin-by-pin reactor calculations [68], (ii) reactor kinetics [69,70], (iii) molten salt fast reactor problems [71,72,73], (iv) problems with feedback from delayed neutron precursors [74,75,76], (v) problems with domain decomposition [77], and (vi) for generation of neutron flux and cross sections for light water reactors [78].…”

Solving the discretised neutron diffusion equations using neural networks

“…Previous work that exploits the linear algebra capabilities of AI processors by using AI libraries to solve scientific problems includes applications in distributed fourier transforms; 17,18 Monte Carlo simulations for finance; 19 many‐body quantum physics; 20 and density functional theory 21 . We have found four examples of previous work which exploit the operations associated with neural networks that are found within AI libraries in order to solve scientific problems 22‐25 . Zhao et al 22 were the first to equate a finite difference discretisation of the Navier‐Stokes equations with a convolutional neural network in which the weights were determined by the discretisation.…”

“…They develop a method of solving the discretised systems based on a combination of a sawtooth multigrid method and the Jacobi method implemented as a U‐Net (a convolutional neural network with a specific architecture 26 ). Using convolutional neural networks with pre‐determined weights, Phillips et al 25 implement an upwind finite volume discretisation and several finite element discretisations arising from a new convolutional finite element method (ConvFEM). The application they study, radiation transport, requires development of a 4D multigrid method (2D in space, 2D in angle), again, based on the U‐Net.…”

Data Reduction in Deterministic Neutron Transport Calculations Using Machine Learning

“…Reducing the computational costs of neutron transport solvers is a point of interest in the field of reactor physics. Many of these methods focus on computational speed up [1][2][3][4], but, given the trajectory of highperformance computing architectures with an inexorable reduction in the memory to compute ratio, the topic of data reduction is also of importance [5]. As an example, the recent work of Cherezov et al takes a data-driven approach to reduce the "expenses associated with the storing, transfer and processing" that is part of a multiphysics reactor simulation [6].…”