Reduced-order modeling of neutron transport separated in energy by Proper Generalized Decomposition with applications to nuclear reactor physics

Dominesey, Kurt A.; Ji, Wei

doi:10.1016/j.jcp.2021.110744

Cited by 8 publications

(3 citation statements)

References 54 publications

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“…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].…”

Section: Introductionmentioning

confidence: 99%

“…A new approach based on data-driven reduced-order models (ROMs) has been gaining popularity in recent years which make use of data-based methodologies to dimensionality reduction. Data-driven models have been developed for (i) linear particle transport problems [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] (ii) nonlinear RT problems [49,50,51,52,53,54,55,56,57,58,59,60], and (iii) various problems in nuclear reactor-physics [61,62,63,64,65,66,67,68,69,70,71]. The fundamental idea behind these ROMs is to leverage databases of solutions to their problems of interest (known a-priori) to develop some reduction in the dimensionality for their involved equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Coale

Anistratov

2023

Journal of Quantitative Spectroscopy and Radiative Transfer

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Coale

Anistratov

2023

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…The proper orthogonal decomposition (POD) type techniques were applied to (1.1) and its time transient counterpart in [8,6,14]. Other related works include space-time POD [13], AP random singular value decomposition (RSVD) [9], dynamic mode decomposition (DMD) [32], proper generalized decomposition (PGD) [17,16,40,3], and dynamical low rank approximations (DLRA) [15,18,36]. These existing approaches either lack the hallmark greedy algorithm or is not a method of snapshots.…”

Section: Introductionmentioning

confidence: 99%

A reduced basis method for radiative transfer equation

Peng

Chen

Cheng

et al. 2021

Preprint

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Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality of the physical and velocity/angular variables and the fact that the problem is multiscale in nature. Leveraging the existence of a hidden low-rank structure hinted by the diffusive limit, in this work, we design and test the angularspace reduced order model for the linear radiative transfer equation, the first such effort based on the celebrated reduced basis method (RBM).Our method is built upon a high-fidelity solver employing the discrete ordinates method in the angular space, an asymptotic preserving upwind discontinuous Galerkin method for the physical space, and an efficient synthetic accelerated source iteration for the resulting linear system. Addressing the challenge of the parameter values (or angular directions) being coupled through an integration operator, the first novel ingredient of our method is an iterative procedure where the macroscopic density is constructed from the RBM snapshots, treated explicitly and allowing a transport sweep, and then updated afterwards. A greedy algorithm can then proceed to adaptively select the representative samples in the angular space and form a surrogate solution space. The second novelty is a least-squares density reconstruction strategy, at each of the relevant physical locations, enabling the robust and accurate integration over an arbitrarily unstructured set of angular samples toward the macroscopic density. Numerical experiments indicate that our method is highly effective for computational cost reduction in a variety of regimes.

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Flow fields prediction for data-driven model of parallel twin cylinders based on POD-RBFNN and POD-BPNN surrogate models

Min,

Jiang

2024

Annals of Nuclear Energy

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Reduced-order modeling of neutron transport separated in energy by Proper Generalized Decomposition with applications to nuclear reactor physics

Cited by 8 publications

References 54 publications

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

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

A reduced basis method for radiative transfer equation

Flow fields prediction for data-driven model of parallel twin cylinders based on POD-RBFNN and POD-BPNN surrogate models

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