Higher order dynamic mode decomposition

Vega, José M.; Clainche, Soledad Le

doi:10.1016/b978-0-12-819743-1.00009-4

Cited by 28 publications

(52 citation statements)

References 48 publications

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“…Results show reconstructions of the current density and the electric field, in the interval (26), within a RRMS error, as defined in Eq. ( 21), ≈1.3 × 10 −4 and ≈1.5 × 10 −3 , respectively, retaining N = 51 modes.…”

Section: Computing the Attractor Via Hodmd Extrapolationmentioning

confidence: 99%

“…Counterpart of Fig. 10 for the application of HODMD to snapshots contained in the timespan (26), with the tunable parameters given in Eq. ( 27).…”

Section: Analysis Of the Periodic Attractor Via Stkdmentioning

confidence: 99%

“…Specifically, the HODMD and STKD methods extract the frequencies and the growth rates of spatiotemporal patterns. Applications to other systems can be found in [26].…”

Section: Introductionmentioning

confidence: 99%

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Uncovering spatiotemporal patterns in semiconductor superlattices by efficient data processing tools

2021

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Time periodic patterns in a semiconductor superlattice, relevant to microwave generation, are obtained upon numerical integration of a known set of drift-diffusion equations. The associated spatiotemporal transport mechanisms are uncovered by applying (to the computed data) two recent data processing tools, known as the higher order dynamic mode decomposition and the spatiotemporal Koopman decomposition. Outcomes include a clear identification of the asymptotic self-sustained oscillations of the current density (isolated from the transient dynamics) and an accurate description of the electric field traveling pulse in terms of its dispersion diagram. In addition, a preliminary version of a data-driven reduced order model is constructed, which allows for extremely fast online simulations of the system response over a range of different configurations.

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Section: Computing the Attractor Via Hodmd Extrapolationmentioning

confidence: 99%

“…Counterpart of Fig. 10 for the application of HODMD to snapshots contained in the timespan (26), with the tunable parameters given in Eq. ( 27).…”

Section: Analysis Of the Periodic Attractor Via Stkdmentioning

confidence: 99%

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Uncovering spatiotemporal patterns in semiconductor superlattices by efficient data processing tools

2021

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“…However, it does not present quasi-periodic behaviour. A deeper explanation about why it does not present quasi-periodic behaviour can be found in Vega & Le Clainche [69].…”

Section: Lorenz Systemmentioning

confidence: 90%

“…It must be remarked that the proposed mathematical model is closed with Neumann boundary conditions. This implies, due to some mathematical properties of the CGLE [69], that no travelling waves can develop, as it could happen with periodic boundary conditions. However, using the Neumann boundary conditions instead of the periodic ones does not compromise the expected dynamical complexity nor decreases the value of the results obtained.…”

Section: Complex Ginzburg-landau Equationmentioning

confidence: 99%

Reduced order models applied to unsteady incompressible fluid flows

Martínez¹

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This Thesis focuses on the developing and concept proofing of a purely data-driven reduced order model (ROM) for its further application to very complex dynamical systems. The ROM will be based on a recent mathematical algorithm, called higher order dynamical mode decomposition (HODMD), which decomposes data sets of unsteady system responses in a collection of spatial modes and their dynamical behaviour defined by their frequencies and growth rates. This decomposition allows for the description of the system response in a semi-analytical form, continuous in time, which can be used to extrapolate future values by direct evaluation. A first ROM concept is applied to the system response of fluid flow around a multi-body array of cylinders at low Reynolds numbers, extrapolating the solution from the early transient stage to the attractor region.A complementary fluid dynamic analysis of the different spatio-temporal modes is carried out by means of the HODMD algorithm to shed light into the highly intricate dynamical response of this unsteady fluid flow. The drawbacks of the primitive ROM version are corrected with the addition of truncation and consistency error estimates of the system response as well as an HODMD interval adaptive law that enforces preliminary checks for the consistency estimate. Ultimately, this improved version is conceptually proved with two different nonlinear dynamical systems such as the Lorenz system and the complex Ginzburg-Landau equation.

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Higher Order Dynamic Mode Decomposition to Model Reacting Flows

Corrochano

D’Alessio

Parente

et al. 2023

Sustainable Aviation

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This work presents a new application of higher order dynamic mode decomposition (HODMD) for the analysis of reactive flows. Due to the high complexity of the data analysed, consisting of more than 80 variables (i.e., temperature and chemically reacting species) a new extension of HODMD has been developed combining the multi-dimensional HODMD algorithm with classical preprocessing techniques generally used in machine learning analyses, such as principal component analysis (PCA). This new methodology has proved to be suitable to identify the main patterns driving the main dynamics of the flow, as well as to develop reduced order models grounded in physical principles. The new algorithm was tested by means of a database obtained from a Computational Fluid Dynamics simulation of an axy-symmetric time varying non-premixed co-flow nitrogen-diluted methane flame, carried out by means of a detailed kinetic mechanism. Different dynamics were identified, and they were associated to the different variables of the reactive flow analysed. Also, this algorithm has been coupled with an additional feature selection step carried out via PCA and varimax rotation. The results that were obtained by coupling PCA with varimax rotation show the outstanding capabilities of this novel methodology to compress original databases as function of the different preprocessing techniques that are used.

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Higher order dynamic mode decomposition

Cited by 28 publications

References 48 publications

Uncovering spatiotemporal patterns in semiconductor superlattices by efficient data processing tools

Uncovering spatiotemporal patterns in semiconductor superlattices by efficient data processing tools

Reduced order models applied to unsteady incompressible fluid flows

Higher Order Dynamic Mode Decomposition to Model Reacting Flows

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