Dynamic Mode Decomposition for Prediction of Kinetic Plasma Behavior

Nayak, Indranil; Teixeira, Fernando L.

doi:10.23919/aces49320.2020.9196070

Cited by 7 publications

(4 citation statements)

References 12 publications

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“…The proper orthogonal decomposition (POD) [10,66] is frequently used to obtain the basis, since the modes ϕ i (x) are orthogonal. Many other modal expansions and bases have been introduced for reduced-order fluid [8,9] and plasma models [67][68][69][70], including balanced POD [71,72], spectral POD [20], dynamic mode decomposition (DMD) [11,12,73], the Koopman decomposition [13,74,75], resolvent analysis [76,77], and autoencoders [32,78,79]. The governing equations are then Galerkin projected onto the basis {ϕ i (x)} by substituting Eq.…”

Section: Projection-based Romsmentioning

confidence: 99%

Promoting global stability in data-driven models of quadratic nonlinear dynamics

Kaptanoglu,

Callaham,

Hansen

et al. 2021

Preprint

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Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of reducedorder models for a variety of scientific and engineering tasks. However, it is challenging to characterize, much less guarantee, the global stability (i.e., long-time boundedness) of these models. The seminal work of Schlegel and Noack [1] provided a theorem outlining necessary and sufficient conditions to ensure global stability in systems with energy-preserving, quadratic nonlinearities, with the goal of evaluating the stability of projection-based models. In this work, we incorporate this theorem into modern data-driven models obtained via machine learning. First, we propose that this theorem should be a standard diagnostic for the stability of projection-based and data-driven models, examining the conditions under which it holds. Second, we illustrate how to modify the objective function in machine learning algorithms to promote globally stable models, with implications for the modeling of fluid and plasma flows. Specifically, we introduce a modified "trapping SINDy" algorithm based on the sparse identification of nonlinear dynamics (SINDy) method. This method enables the identification of models that, by construction, only produce bounded trajectories. The effectiveness and accuracy of this approach are demonstrated on a broad set of examples of varying model complexity and physical origin, including the vortex shedding in the wake of a circular cylinder.

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Section: Projection-based Romsmentioning

confidence: 99%

Promoting global stability in data-driven models of quadratic nonlinear dynamics

Kaptanoglu,

Callaham,

Hansen

et al. 2021

Preprint

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“…It is noted that the DMD method has been also applied to plasma physics [7][8][9][10], most notably by Taylor et al [11] and Kaptanoglu et al [12] in a z-pinch experimental configuration. These two latter studies provided interpretable insights into the dominant patterns of activity of the z-pinch experiment.…”

Section: Introductionmentioning

confidence: 99%

Dynamic mode decomposition for data-driven analysis and reduced-order modeling of E × B plasmas: I. Extraction of spatiotemporally coherent patterns

Faraji,

Reza,

Knoll

et al. 2023

J. Phys. D: Appl. Phys.

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The advent of data-driven/machine-learning based methods and the increase in data available from high-fidelity simulations and experiments has opened new pathways toward realizing reduced-order models for plasma systems that can aid in explaining the complex, multi-dimensional phenomena and enable forecasting and prediction of the systems’ behavior. In this two-part article, we evaluate the utility and the generalizability of the dynamic mode decomposition (DMD) algorithm for data-driven analysis and reduced-order modeling of plasma dynamics in cross-field E × B configurations. The DMD algorithm is an interpretable data-driven method that finds a best-fit linear model describing the time evolution of spatiotemporally coherent structures (patterns) in data. We have applied the DMD to extensive high-fidelity datasets generated using a particle-in-cell (PIC) code based on the cost-efficient reduced-order PIC scheme. In this part, we first provide an overview of the concept of DMD and its underpinning proper orthogonal and singular value decomposition methods. Two of the main DMD variants are next introduced. We then present and discuss the results of the DMD application in terms of the identification and extraction of the dominant spatiotemporal modes from high-fidelity data over a range of simulation conditions. We demonstrate that the DMD variant based on variable projection optimization (OPT-DMD) outperforms the basic DMD method in identification of the modes underlying the data, leading to notably more reliable reconstruction of the ground-truth. Furthermore, we show in multiple test cases that the discrete frequency spectrum of OPT-DMD-extracted modes is consistent with the temporal spectrum from the fast Fourier transform of the data. This observation implies that the OPT-DMD augments the conventional spectral analyses by being able to uniquely reveal the spatial structure of the dominant modes in the frequency spectra, thus, yielding more accessible, comprehensive information on the spatiotemporal characteristics of the plasma phenomena.

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“…Some of these dynamics are highly nonlinear, and can occur on fast time scales and small spatial scales where many analytic assumptions break down. The reality of fast time scales requires that many real-time plasma control schemes are limited to simple models such as those based on 1D transport [7], linearization or local-expansions [8][9][10][11][12][13][14][15][16], heuristics (based on prior experimental knowledge) [17,18], the biorthogonal decomposition [19][20][21][22][23][24], and so forth. Despite the challenges posed by multiscale dynamics and nonlinearity, many of these models have been successfully employed for real-time control in operational scenarios.…”

Section: Introductionmentioning

confidence: 99%

Exploring data-driven models for spatiotemporally local classification of Alfvén eigenmodes

Kaptanoglu¹,

Jalalvand²,

Garcia³

et al. 2022

Nucl. Fusion

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Alfvén eigenmodes (AEs) are an important and complex class of plasma dynamics commonly observed in tokamaks and other plasma devices. In this work, we manually labeled a small database of 26 discharges from the DIII-D tokamak in order to train simple neural-network-based models for classifying AEs. The models provide spatiotemporally local identification of four types of Alfvén eigenmodes by using an array of 40 electron cyclotron emission (ECE) signals as inputs. Despite the minimal dataset, this strategy performs well at spatiotemporally localized classification of Alfvén eigenmodes, indicating future opportunities for more sophisticated models and incorporation into real-time control strategies. The trained model is then used to generate spatiotemporally-resolved labels for each of the forty ECE measurements on a much larger database of 1,112 DIII-D discharges. This large set of precision labels can be used in future studies for advanced deep predictors and new physical insights.

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Dynamic Mode Decomposition for Prediction of Kinetic Plasma Behavior

Cited by 7 publications

References 12 publications

Promoting global stability in data-driven models of quadratic nonlinear dynamics

Promoting global stability in data-driven models of quadratic nonlinear dynamics

Dynamic mode decomposition for data-driven analysis and reduced-order modeling of E × B plasmas: I. Extraction of spatiotemporally coherent patterns

Exploring data-driven models for spatiotemporally local classification of Alfvén eigenmodes

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