Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

Choi, Youngsoo; Brown, Peter N.; Arrighi, William; Anderson, Robert; Huynh, Kevin

doi:10.1016/j.jcp.2020.109845

Cited by 69 publications

(34 citation statements)

References 27 publications

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“…Since the exact error associated with the reduced-order model cannot be computed without the Hi-Fi solution, an error estimate is used. Based on the type of underlying PDE several a posteriori error estimators [38][39][40][41][42], which are relevant to MOR, were developed in the past. Most of the estimators used in [26][27][28][29][30][31][32][33][36][37][38][39][40][41]43,44] focused on the affine parameter dependency of the Hi-Fi model, which resulted in an offline/online decomposition approach: expensive computations of lower-order matrices are done offline while the norm of the residual for any given parameter configuration was computed online with a minimal effort.…”

Section: Overviewmentioning

confidence: 99%

Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

et al. 2021

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This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach, which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires us to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and trigger the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution.

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Section: Overviewmentioning

confidence: 99%

Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

et al. 2021

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“…A reduced order model (ROM) that aims to produce a low-dimensional representation of FOM could be an alternative to handling field-scale inverse problems, optimization, or real-time reservoir management (Schilders et al, 2008;Amsallem et al, 2015;Choi et al, 2019;Choi, Boncoraglio, et al, 2020;McBane & Choi, 2021;Yoon, Oostrom, et al, 2009). The ROM methodology primarily relies on the parameterization of a problem (i.e., repeated evaluations of a problem depending on parameters), which could correspond to physical properties, geometric characteristics, or boundary conditions (Ballarin et al, 2019;Venturi et al, 2019;Hesthaven et al, 2016;Hoang et al, 2021;Copeland et al, 2021;Choi, Coombs, & Anderson, 2020;Carlberg et al, 2018). However, it is difficult to parameterize heterogeneous spatial fields of PDE coefficients such as heterogeneous material properties by a few parameters.…”

Section: Introductionmentioning

confidence: 99%

Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties

Kadeethum,

O'Malley,

Choi

et al. 2021

Preprint

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“…Generally, these matrices are small enough for the methods to be computationally efficient. For parametrised time-dependent problems, Choi et al [35] developed a space-time reduced-order model for radiation transport, implementing an incremental SVD and exploiting the block structure of the space-time reduced basis for efficiency. Applied to problems with billions of degrees of freedom in energy, space, and time, this method was demonstrated to be accurate with relatively few basis functions and had good computational speed-up factors.…”

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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Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

Cited by 69 publications

References 27 publications

Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties

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

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