Affine reduced-order model for radiation transport problems in cylindrical coordinates

Tano, Mauricio; Ragusa, Jean C.; Caron, Dominic; Behne, Patrick

doi:10.1016/j.anucene.2021.108214

Cited by 11 publications

(2 citation statements)

References 28 publications

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“…Typically, proper orthogonal decomposition (POD) [13] or non-linear manifold learning via artificial neural networks (ANNs) [14] are used for computing the reduced set of modes. Then, intrusive ROMs use the computed modes for truncating, e.g., balanced truncation method [15], projecting, e.g., Galerkin or Petrov-Galerkin projections [16,17], or moment-matching, e.g., moment-matching method [18], the high-fidelity discretized system of equations into a reduced representation. Thanks to the temporal and parametric affinity of the high-fidelity model or by gappy-sampling of the nonlinear parametric terms, e.g., via the Discrete Empirical Interpolation Method [19], intrusive ROMs preserve temporal and parametric dependence and, thus, have been effectively used as surrogate models in multi-query problems [20].…”

Section: Introductionmentioning

confidence: 99%

Parametric Dynamic Mode Decomposition for Reduced Order Modeling

Huhn¹,

Tano²,

Ragusa³

et al. 2022

Preprint

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Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiples parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. In this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigenpair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

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Section: Introductionmentioning

confidence: 99%

Parametric Dynamic Mode Decomposition for Reduced Order Modeling

Huhn¹,

Tano²,

Ragusa³

et al. 2022

Preprint

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“…Along the line of low rank algorithms based on tensor decomposition, dynamical low rank algorithm (DLRA) [35,14,34]and the proper generalized decomposition (PGD) [1,37,13] have been designed. Projection based ROMs have also been actively developed in the recent few years, for example the proper orthogonal decomposition (POD) and its variations [5,11,12,40,3,10,19], the dynamical mode decomposition (DMD) [26,27]. Among those work, the POD methods in [5,41,19] and our previous work in reduced basis method (RBM) for the steady state problem [30] make explicit use of the low rank structure of the solution manifold induced by the angular variable, namely, the ROM built is based on treating the angular variable as the "parameter" of the model.…”

Section: Introductionmentioning

confidence: 99%

A micro-macro decomposed reduced basis method for the time-dependent radiative transfer equation

Peng¹,

Chen²,

Cheng³

et al. 2022

Preprint

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Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building reduced order models (ROM) by analytical methods. In recent years, there is a surge of interest in developing ROM using data-driven or computational tools that offer more applicability and flexibility. This paper is a work towards that direction.Motivated by our previous work of designing ROM for the stationary radiative transfer equation in [30] by leveraging the low-rank structure of the solution manifold induced by the angular variable, we here further advance the methodology to the time-dependent model. Particularly, we take the celebrated reduced basis method (RBM) approach and propose a novel micro-macro decomposed reduced basis method (MMD-RBM). The MMD-RBM is constructed by exploiting, in a greedy fashion, the low-rank structures of both the micro-and macro-solution manifolds with respect to the angular and temporal variables. Our reduced order surrogate consists of: reduced bases for reduced order subspaces and a reduced quadrature rule in the angular space. The proposed MMD-RBM features several structure-preserving components: 1) an equilibrium-respecting strategy to construct reduced order subspaces which better utilize the structure of the decomposed system, and 2) a recipe for preserving positivity of the quadrature weights thus to maintain the stability of the underlying reduced solver. The resulting ROM can be used to achieve a fast online solve for the angular flux in angular directions outside the training set and for arbitrary order moment of the angular flux.

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Parametric model-order reduction for radiation transport using multi-resolution proper orthogonal decomposition

Behne

Ragusa

2023

Annals of Nuclear Energy

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Affine reduced-order model for radiation transport problems in cylindrical coordinates

Cited by 11 publications

References 28 publications

Parametric Dynamic Mode Decomposition for Reduced Order Modeling

Parametric Dynamic Mode Decomposition for Reduced Order Modeling

A micro-macro decomposed reduced basis method for the time-dependent radiative transfer equation

Parametric model-order reduction for radiation transport using multi-resolution proper orthogonal decomposition

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