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

Cited by 22 publications

(8 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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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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“…, and Π ∈ R n×n is the permutation matrix containing information about the first k chosen sensors [56]- [58]. In unconstrained QR pivoting, the (k + 1) st iteration selects a column from the submatrix R (k) 22 with the maximal two-norm, then swaps the selected column with the (k + 1) st column while updating permutation indices…”

Section: B Column-pivoted Qr Decomposition With Spatial Constraintsmentioning

confidence: 99%

“…Constraints are integrated within this step, by forcing the pivot column index to be selected from the latest set of allowable indices based on the constraints under consideration. The k + 1 st iteration in constrained optimization selects the pivot column with largest 2 norm, r (k) 22 (i) , from the constrained/unconstrained set of allowable column indices in R (k) 22 . The QR pivoting algorithm results in the following diagonal dominance structure in R:…”

Section: B Column-pivoted Qr Decomposition With Spatial Constraintsmentioning

confidence: 99%

“…Nuclear applications require this ability to accurately simulate high-dimensional fields with minimal computational resources and without the complexity of fullorder models [13], [14]. Projection-based ROMs, which represent high-fidelity physics using low-rank/data-driven modal decompositions, have been widely adopted for modeling fluids and turbulence [15]- [19] and nuclear core composition [20]- [22]. Such modal decompositions are closely related to empirical orthogonal functions for surrogate models in atmospheric sciences [23], [24], electrodynamics [25], [26] and heat transfer [27], [28]; as well as model reduction of stochastic processes [29] and balanced model reduction for optimal control [30], [31].…”

Section: Introductionmentioning

confidence: 99%

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Constrained Optimization of Sensor Placement for Nuclear Digital Twins

Karnik,

Abdo,

Estrada-Perez

et al. 2024

IEEE Sensors J.

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The deployment of extensive sensor arrays in nuclear reactors is infeasible due to challenging operating conditions and inherent spatial limitations. Strategically placing sensors within defined spatial constraints is essential for the reconstruction of reactor flow fields and the creation of nuclear digital twins. We develop a data-driven technique that incorporates constraints into an optimization framework for sensor placement, with the primary objective of minimizing reconstruction errors under noisy sensor measurements. The proposed greedy algorithm optimizes sensor locations over high-dimensional grids, adhering to user-specified constraints. We demonstrate the efficacy of optimized sensors by exhaustively computing all feasible configurations for a low-dimensional dynamical system. To validate our methodology, we apply the algorithm to the Out-of-Pile Testing and Instrumentation Transient Water Irradiation System (OPTI-TWIST) prototype capsule. This capsule is electrically heated to emulate the neutronics effect of the nuclear fuel. The TWIST prototype that will eventually be inserted in the Transient Reactor Test facility (TREAT) at the Idaho National Laboratory (INL), serves as a practical demonstration. The resulting sensor-based temperature reconstruction within OPTI-TWIST demonstrates minimized error, provides probabilistic bounds for noise-induced uncertainty, and establishes a foundation for communication between the digital twin and the experimental facility.

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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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Modeling isotopic evolution with surrogates based on dynamic mode decomposition

Cited by 22 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

Constrained Optimization of Sensor Placement for Nuclear Digital Twins

Acceleration of the Power Method with Dynamic Mode Decomposition

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