Modeling isotopic evolution with surrogates based on dynamic mode decomposition

Abdo, Mohammad; Elzohery, Rabab; Roberts, Jeremy A.

doi:10.1016/j.anucene.2019.01.048

Annals of Nuclear Energy

2019

DOI: 10.1016/j.anucene.2019.01.048

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Modeling isotopic evolution with surrogates based on dynamic mode decomposition

Mohammad Abdo

Rabab Elzohery

Jeremy A. Roberts

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Cited by 20 publications

(2 citation statements)

References 5 publications

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“…The source was intentionally 13 located off-center to activate the asymmetric harmonics. The source intensity was 8000 neutrons/s 14. Neutrons were detected at 44 points, as indicated in Fig.1.…”

mentioning

confidence: 90%

Higher harmonic analyses of the Rossi-α method and application of dynamic mode decomposition for time decay constant determination in a 1D subcritical system

Yamamoto

Sakamoto²

2022

Annals of Nuclear Energy

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mentioning

confidence: 90%

Higher harmonic analyses of the Rossi-α method and application of dynamic mode decomposition for time decay constant determination in a 1D subcritical system

Yamamoto

Sakamoto²

2022

Annals of Nuclear Energy

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“…For example, DMD was used to recover α eigenvalues from time-dependent, neutron transport calculations [13]. Others have used DMD as a direct, explicit-in-time surrogate for such black-box models, e.g., to model the evolution of nuclear reactor isotopics over long time periods [2,9], the nonlinear response of reactor power during short transients [1], and nuclear-fuel, decay-heat generation [3].…”

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confidence: 99%

Acceleration of the Power Method with Dynamic Mode Decomposition

Roberts

Elzohery

et al. 2019

Nuclear Science and Engineering

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Presented is an algorithm based on dynamic mode decomposition (DMD) for acceleration of the power method (PM). The power method is a simple technique for determining the dominant eigenmode of an operator A, and variants of the power method are widely used in reactor analysis. Dynamic mode decomposition is an algorithm for decomposing a time-series of spatially-dependent data and producing an explicit-in-time reconstruction for that data. By viewing successive power-method iterates as snapshots of a time-varying system tending toward a steady state, DMD can be used to predict that steady state using (a sometime surprisingly small) n iterates. The process of generating snapshots with the power method and extrapolating forward with DMD can be repeated. The resulting restarted, DMD-accelerated power method (or DMD-PM(n)) was applied to the two-dimensional IAEA diffusion benchmark and compared to the unaccelerated power method and Arnoldi's method. Results indicate that DMD-PM(n) can reduce the number of power iterations required by approximately a factor of 5. However, Arnoldi's method always outperformed DMD-PM(n) for an equivalent number of matrix-vector products Av. In other words, DMD-PM(n) cannot compete with leading eigensolvers if one is not limited to snapshots produced by the power method. Contrarily, DMD-PM(n) can be readily applied as a post process to existing power-method applications for which Arnoldi and similar methods are not directly applicable. A slight variation of the method was also found to produce reasonable approximations to the first and second harmonics without substantially affecting convergence of the dominant mode.

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Uncertainty and regression analysis of the MSLB accident in PWR based on unscented transformation and low rank approximation

Foad

Yamamoto

Endo

2020

Annals of Nuclear Energy

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Modeling isotopic evolution with surrogates based on dynamic mode decomposition

Cited by 20 publications

References 5 publications

Higher harmonic analyses of the Rossi-α method and application of dynamic mode decomposition for time decay constant determination in a 1D subcritical system

Higher harmonic analyses of the Rossi-α method and application of dynamic mode decomposition for time decay constant determination in a 1D subcritical system

Acceleration of the Power Method with Dynamic Mode Decomposition

Uncertainty and regression analysis of the MSLB accident in PWR based on unscented transformation and low rank approximation

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