An autoencoder‐based reduced‐order model for eigenvalue problems with application to neutron diffusion

Phillips, Toby R. F.; Heaney, Claire E.; Smith, Paul N.; Pain, Christopher C.

doi:10.1002/nme.6681

Cited by 50 publications

(28 citation statements)

References 59 publications

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“…Future work will explore the use of autoencoders to form the low-dimensional space. This could improve the accuracy of the ROMs, as the nonlinearity of the autoencoder can be advantageous [31].…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2021

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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.

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Section: Discussionmentioning

confidence: 99%

“…These values are then passed back into the inner iterations until either k eff converges, with a tolerance of 10 −8 , or the maximum number of iterations is reached, 200. These algorithms are given in [31] and repeated here for completeness.…”

Section: The Power Methodsmentioning

confidence: 99%

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

et al. 2021

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“…In order to do this, we must find the matrices A R (θ, h), B R (θ, h), which correspond to the arbitrary parameter values θ and h. As previously mentioned, to calculate the high-fidelity matrix for the parameters θ, h and then project it onto the basis functions would be too expensive, as it involves assembling N DoF by N DoF matrices. To approximate these matrices we interpolate between the pre-calculated sets of reduced-order matrices listed in (24). We first find the two heights in the set of parameters that are closest to h, i.e., find…”

Section: Global Proper Orthogonal Decompositionmentioning

confidence: 99%

“…Early work shows that autoencoders are able to capture more accurately the physics in advectiondominated problems [21,22], which are known to have slowly decaying Kolmogorov n widths or slowly decaying singular values [23]. Phillips et al [24] used an autoencoder to find the reduced basis for a projection-based ROM applied to the neutron diffusion equation. For reductions to very low-dimensional spaces, the autoencoder outperformed POD.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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“…A recent dimensionality reduction method that combines POD/SVD and an autoencoder (SVD-AE), has been introduced independently by a number of researchers and demonstrated on: vortex-induced vibrations of a flexible offshore riser at high Reynolds number [49] (described as hybrid ROM); the generalised eigenvalue problems associated with neutron diffusion [50] (described as an SVD autoencoder); Marsigli flow [51] (described as nonlinear POD); and cardiac electrophysiology [52] (described as POD-enhanced deep learning ROM). This method has at least three advantages: (i) by training the autoencoder with POD coefficients, it is of no consequence whether the snapshots are associated with a structured or unstructured mesh; (ii) an initial reduction of the number of variables by applying POD means that the autoencoder will have fewer trainable parameters and therefore be easier to train; and (iii) autoencoders in general can find the minimum number of latent variables needed in the reduced representation.…”

Section: Introductionmentioning

confidence: 99%

An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes

Heaney,

Wolffs,

Tómasson

et al. 2022

Preprint

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The modelling 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 kilometres versus 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 nonintrusive 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 explore several types of autoencoder networks, known for their ability to compress information accurately and compactly. The performance of the autoencoders is assessed on 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 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. Statistics of the flows obtained from the CFD simulations are compared to those of the AI-DDNIROM predictions to demonstrate the success of our approach.

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An autoencoder‐based reduced‐order model for eigenvalue problems with application to neutron diffusion

Cited by 50 publications

References 59 publications

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

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

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

An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes

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