Reduced-Order Modelling Applied to the Multigroup Neutron Diffusion Equation Using a Nonlinear Interpolation Method for Control-Rod Movement

Producing high-fidelity real-time simulations of neutron diffusion in a reactor is computationally extremely challenging, due, in part, to multiscale behaviour in energy and space. In many scientific fields, including nuclear modelling, the application of reduced-order modelling can lead to much faster computation times without much loss of accuracy, paving the way for real-time simulation as well as multi-query problems such as uncertainty quantification and data assimilation. This paper compares two reduced-order models that are applied to model the movement of control rods in a fuel assembly for a given temperature profile. The first is a standard approach using proper orthogonal decomposition (POD) to generate global basis functions, and the second, a new method, uses POD but produces global basis functions that are local in the parameter space (associated with the control-rod height). To approximate the eigenvalue problem in reduced space, a novel, nonlinear interpolation is proposed for modelling dependence on the control-rod height. This is seen to improve the accuracy in the predictions of both methods for unseen parameter values by two orders of magnitude for keff and by one order of magnitude for the scalar flux

Solving the discretised neutron diffusion equations using neural networks

This paper presents a new approach which uses the tools within artificial intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical methods. In particular, we describe how to represent numerical discretisations arising from the finite volume and finite element methods by pre-determining the weights of convolutional layers within a neural network. As the weights are defined by the discretisation scheme, no training of the network is required and the solutions obtained are identical (accounting for solver tolerances) to those obtained with standard codes often written in Fortran or C++. We also explain how to implement the Jacobi method and a multigrid solver using the functions available in AI libraries. For the latter, we use a U-Net architecture which is able to represent a sawtooth multigrid method. A benefit of using AI libraries in this way is that one can exploit their built-in technologies to enable the same code to run on different computer architectures (such as central processing units, graphics processing units or new-generation AI processors) without any modification. In this article, we apply the proposed approach to eigenvalue problems in reactor physics where neutron transport is described by diffusion theory. For a fuel assembly benchmark, we demonstrate that the solution obtained from our new approach is the same (accounting for solver tolerances) as that obtained from the same discretisation coded in a standard way using Fortran. We then proceed to solve a reactor core benchmark using the new approach. For both benchmarks we give timings for the neural network implementation run on a CPU and a GPU, and a serial Fortran code run on a CPU

Data assimilation predictive GAN (DA-PredGAN) applied to a spatio-temporal compartmental model in epidemiology

We propose a novel use of generative adversarial networks (GANs) (i) to make predictions in time (PredGAN) and (ii) to assimilate measurements (DA-PredGAN). In the latter case, we take advantage of the natural adjoint-like properties of generative models and the ability to simulate forwards and backwards in time. GANs have received much attention recently, after achieving excellent results for their generation of realistic-looking images. We wish to explore how this property translates to new applications in computational modelling and to exploit the adjoint-like properties for efficient data assimilation. We apply these methods to a compartmental model in epidemiology that is able to model space and time variations, and that mimics the spread of COVID-19 in an idealised town. To do this, the GAN is set within a reduced-order model, which uses a low-dimensional space for the spatial distribution of the simulation states. Then the GAN learns the evolution of the low-dimensional states over time. The results show that the proposed methods can accurately predict the evolution of the high-fidelity numerical simulation, and can efficiently assimilate observed data and determine the corresponding model parameters

A domain decomposition non-intrusive reduced order model for turbulent flows

In this paper, a new Domain Decomposition Non-Intrusive Reduced Order Model (DDNIROM) is developed for turbulent flows. The method works by partitioning the computational domain into a number of subdomains in such a way that the summation of weights associated with the finite element nodes within each subdomain is approximately equal, and the communication between subdomains is minimised. With suitably chosen weights, it is expected that there will be approximately equal accuracy associated with each subdomain. This accuracy is maximised by allowing the partitioning to occur through areas of the domain that have relatively little flow activity, which, in this case, is characterised by the pointwise maximum Reynolds stresses.A Gaussian Process Regression (GPR) machine learning method is used to construct a set of local approximation functions (hypersurfaces) for each subdomain. Each local hypersurface represents not only the fluid dynamics over the subdomain it belongs to, but also the interactions of the flow dynamics with the surrounding subdomains. Thus, in this way, the surrounding subdomains may be viewed as providing boundary conditions for the current subdomain.We consider a specific example of turbulent air flow within an urban neighbourhood at a test site in London and demonstrate the effectiveness of the proposed DDNIROM

The frequency of osteogenic activities and the pattern of intermittence between periods of physical activity and sedentary behaviour affects bone mineral content: the cross-sectional NHANES study

BACKGROUND: Sedentary behaviours, defined as non exercising seated activities, have been shown to have deleterious effects on health. It has been hypothesised that too much sitting time can have a detrimental effect on bone health in youth. The aim of this study is to test this hypothesis by exploring the association between objectively measured volume and patterns of time spent in sedentary behaviours, time spent in specific screen-based sedentary pursuits and bone mineral content (BMC) accrual in youth. METHODS: NHANES 2005–2006 cycle data includes BMC of the femoral and spinal region via dual-energy X-ray absorptiometry (DEXA), assessment of physical activity and sedentary behaviour patterns through accelerometry, self reported time spent in screen based pursuits (watching TV and using a computer), and frequency of vigorous playtime and strengthening activities. Multiple regression analysis, stratified by gender was performed on N = 671 males and N = 677 females aged from 8 to 22 years. RESULTS: Time spent in screen-based sedentary behaviours is negatively associated with femoral BMC (males and females) and spinal BMC (females only) after correction for time spent in moderate and vigorous activity. Regression coefficients indicate that an additional hour per day of screen-based sitting corresponds to a difference of −0.77 g femoral BMC in females [95% CI: -1.31 to −0.22] and of −0.45 g femoral BMC in males [95% CI: -0.83 to −0.06]. This association is attenuated when self-reported engagement in regular (average 5 times per week) strengthening exercise (for males) and vigorous playing (for both males and females) is taken into account. Total sitting time and non screen-based sitting do not appear to have a negative association with BMC, whereas screen based sedentary time does. Patterns of intermittence between periods of sitting and moderate to vigorous activity appears to be positively associated with bone health when activity is clustered in time and inter-spaced with long continuous bouts of sitting. CONCLUSIONS: Some specific sedentary pursuits (screen-based) are negatively associated with bone health in youth. This association is specific to gender and anatomical area. This relationship between screen-based time and bone health is independent of the total amount of physical activity measured objectively, but not independent of self-reported frequency of strengthening and vigorous play activities. The data clearly suggests that the frequency, rather than the volume, of osteogenic activities is important in counteracting the effect of sedentary behaviour on bone health. The pattern of intermittence between sedentary periods and activity also plays a role in bone accrual, with clustered short bouts of activity interspaced with long periods of sedentary behaviours appearing to be more beneficial than activities more evenly spread in time

A reduced order model for turbulent flows in the urban environment using machine learning

To help create a comfortable and healthy indoor and outdoor environment in which to live, there is a need to understand turbulent air flows within the urban environment. To this end, building on a previously reported method [1], we develop a fast-running Non-Intrusive Reduced Order Model (NIROM) for predicting the turbulent air flows found within an urban environment. To resolve larger scale turbulent fluctuations, we employ a Large Eddy Simulation (LES) model and solve the resulting computational model on unstructured meshes. The objective is to construct a rapid-running NIROM from these results that will have ‘similar’ dynamics to the original LES model. Based on Proper Orthogonal Decomposition (POD) and machine learning techniques, this Reduced Order Model (ROM) is six orders of magnitude faster than the high-fidelity LES model and we demonstrate how ‘similar’ it can be to the high-fidelity model by comparing statistical quantities such as the mean flows, Reynolds stresses and probability densities of the velocities. We also include validation of the high-fidelity model against data from wind tunnel experiments.This paper represents a key step towards the use of reduced order modelling for operational purposes with the tantalising possibility of it being used in place of Gaussian plume models, and the potential for greatly improved model fidelity and confidence

Longevity of daily oral Vitamin D3 supplementation:Differences in 25OHD and 24,25(OH)2D observed 2 years after cessation of a 1-year randomized controlled trial (VICtORy RECALL)

Purpose To determine the longevity of vitamin D status following cessation of vitamin D3 supplementation, 2 and 3 years after a 1 year randomised double blind placebo controlled trial: (Vitamin D and Cardiovascular Risk (VICtORY)); and to investigate possible predictive factors. Method Of the 305 Caucasian non-smoking postmenopausal women randomised to ViCtORY (2009-2010), participants who had not taken vitamin D supplements since the trial ended were invited to attend follow up visits. Total 25-hydroxyvitamin D (25OHD) and 24,25-dihydroxyvitamin D (24,25OH2D) were measured by dual tandem mass spectrometry of serum samples following removal of protein and de-lipidation; the original RCT samples were re-analysed simultaneously. Vitamin D binding protein (VDBP) was measured by monoclonal immunoassay. Results In March 2012 and March 2013, 159 women (mean (SD) age 67.6 (2.1) years) re-attended, distributed between the original treatment groups: daily vitamin D3 400IU; 1000IU; and placebo. One month after the RCT ended (March 2010) the proportion of women in placebo, 400IU, and 1000IU vitamin D3 groups, respectively, with 25OHD0.001, n=46,44,54); 42%, 33%, 12% (2y, p=0.002,n=50,48,57) and 45%, 27%, 29% (3y, p=0.138, n=47,45,51,). VDBP was a predictor of circulating 25OHD longevity (beta for VDBP in µg/ml:0.736; 95% CI 0.216-1.255,p=0.006) but not 24,25OH2D

An AI-based non-intrusive reduced-order model for extended domains applied to multiphase flow in pipes

The modeling of multiphase flow in a pipe presents a significant challenge for high-resolution computational fluid dynamics (CFD) models due to the high aspect ratio (length over diameter) of the domain. In subsea applications, the pipe length can be several hundreds of meters vs a pipe diameter of just a few inches. Approximating CFD models in a low-dimensional space, reduced-order models have been shown to produce accurate results with a speed-up of orders of magnitude. In this paper, we present a new AI-based non-intrusive reduced-order model within a domain decomposition framework (AI-DDNIROM), which is capable of making predictions for domains significantly larger than the domain used in training. This is achieved by (i) using a domain decomposition approach; (ii) using dimensionality reduction to obtain a low-dimensional space in which to approximate the CFD model; (iii) training a neural network to make predictions for a single subdomain; and (iv) using an iteration-by-subdomain technique to converge the solution over the whole domain. To find the low-dimensional space, we compare Proper Orthogonal Decomposition with several types of autoencoder networks, known for their ability to compress information accurately and compactly. The comparison is assessed with two advection-dominated problems: flow past a cylinder and slug flow in a pipe. To make predictions in time, we exploit an adversarial network, which aims to learn the distribution of the training data, in addition to learning the mapping between particular inputs and outputs. This type of network has shown the potential to produce visually realistic outputs. The whole framework is applied to multiphase slug flow in a horizontal pipe for which an AI-DDNIROM is trained on high-fidelity CFD simulations of a pipe of length 10 m with an aspect ratio of 13:1 and tested by simulating the flow for a pipe of length 98 m with an aspect ratio of almost 130:1. Inspection of the predicted liquid volume fractions shows a good match with the high fidelity model as shown in the results. Statistics of the flows obtained from the CFD simulations are compared to those of the AI-DDNIROM predictions to demonstrate the accuracy of our approach

Identification of hip fracture patients from radiographs using Fourier analysis of the trabecular structure: a cross-sectional study

Peer reviewedPublisher PD