Sparsity-promoting dynamic mode decomposition

Jovanović, Mihailo R.; Schmid, Peter J.; Nichols, Joseph W.

doi:10.1063/1.4863670

Cited by 720 publications

(629 citation statements)

References 42 publications

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“…Further, the DMDc method is well suited to couple with innovative sparsity-promoting sampling and control strategies [8,42,4,12]. This connection has already been demonstrated for DMD both in time and space [6,22,53]. DMDc is therefore positioned to have a dramatic effect on the analysis and control of large-scale complex systems.…”

Section: Connections To System Identification Methodsmentioning

confidence: 99%

“…Second, DMD has acquired popularity as a method for systems with nonlinear dynamics, due to a strong connection between DMD and Koopman operator theory [29,32,41,7,33]. Finally, DMD can be modified to take advantage of sparse, or limited, measurements of the complex system [6,53,22]. Sparse measurements have recently been leveraged in a variety of complex systems-some for control [4,42,30,12].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Mode Decomposition with Control

Proctor¹,

Brunton²,

Kutz³

2016

SIAM J. Appl. Dyn. Syst.

777

515

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Abstract. We develop a new method which extends dynamic mode decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear analysis to nonlinear operator theory, and provides an equation-free architecture which is compatible with compressive sensing. In actuated systems, DMD is incapable of producing an input-output model; moreover, the dynamics and the modes will be corrupted by external forcing. Our new method, dynamic mode decomposition with control (DMDc), capitalizes on all of the advantages of DMD and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models. The method is data-driven in that it does not require knowledge of the underlying governing equations-only snapshots in time of observables and actuation data from historical, experimental, or black-box simulations. We demonstrate the method on high-dimensional dynamical systems, including a model with relevance to the analysis of infectious disease data with mass vaccination (actuation).

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Section: Connections To System Identification Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic Mode Decomposition with Control

Proctor¹,

Brunton²,

Kutz³

2016

SIAM J. Appl. Dyn. Syst.

777

515

View full text Add to dashboard Cite

show abstract

“…Two modes, mode 2 and mode 3, are highlighted in the figure and are selected for further analysis, as they describe a substantial part of the processed data sequence. The choice and amplitudes of these modes are determined using the optimization algorithm described in [21], and the resulting amplitude distribution is shown versus the detected frequencies in Figure 8(b). As demonstrated in [11], these two modes coincide with the fundamental Tollmien-Schlichting and subharmonic modes of the early transitional regime.…”

Section: Transition To Turbulence In a Compressible Flat-plate Boundamentioning

confidence: 99%

“…The resulting eigenvalues and spectrum are shown in Figure 6, where six modes are highlighted excluding the mean. These modes are selected using the sparsity promoting algorithm of [21]. The full decomposition is performed using 120 processors in 149 seconds.…”

Section: Transition To Turbulence In a Compressible Separated Boundarmentioning

confidence: 99%

Parallel data-driven decomposition algorithm for large-scale datasets: with application to transitional boundary layers

Sayadi

Schmid

2016

Theor. Comput. Fluid Dyn.

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Many fluid flows of engineering interest, though very complex in appearance, can be approximated by low-order models governed by a few modes, able to capture the dominant behavior (dynamics) of the system. This feature has fueled the development of various methodologies aimed at extracting dominant coherent structures from the flow. Some of the more general techniques are based on data-driven decompositions, most of which rely on performing a singular value decomposition (SVD) on a formulated snapshot (data) matrix. The amount of experimentally or numerically generated data expands as more detailed experimental measurements and increased computational resources become readily available. Consequently, the data-matrix to be processed will consist of far more rows than columns, resulting in a so-called tall-and-skinny (TS) matrix. Ultimately, the SVD of such a TS data-matrix can no longer be performed on a single processor and parallel algorithms are necessary. The present study employs the parallel TSQR algorithm of [1], which is further used as a basis of the underlying parallel SVD. This algorithm is shown to scale well on machines with a large number of processors and, therefore, allows the decomposition of very large data-sets. In addition, the simplicity of its implementation and the minimum required communication makes it suitable for integration in existing numerical solvers and data-decomposition techniques. Examples that demonstrate the capabilities of highly parallel datadecomposition algorithms include transitional processes in compressible boundary layers without and with induced flow separation.

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“…Wavelet analysis reveals intermittency as an important characteristic of sound sources [158], as different source modes may continually interfere with one another. For flows containing strong tonal components, dynamic mode decomposition [159] and its sparsity-promoting variant [160] enable extraction of coherent dynamics from a sequence of snapshots with minimal spectral leakage.…”

Section: (A) Trends In Hpc: Towards Exascale Computingmentioning

confidence: 99%

A second golden age of aeroacoustics?

Lele

Nichols

2014

Phil. Trans. R. Soc. A.

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In 1992, Sir James Lighthill foresaw the dawn of a second golden age in aeroacoustics enabled by computer simulations (Hardin JC, Hussaini MY (eds) 1993 Computational aeroacoustics, New York, NY: Springer (doi:10.1007). This review traces the progress in large-scale computations to resolve the noise-source processes and the methods devised to predict the far-field radiated sound using this information. Keeping focus on aviation-related noise sources a brief account of the progress in simulations of jet noise, fan noise and airframe noise is given highlighting the key technical issues and challenges. The complex geometry of nozzle elements and airframe components as well as the high Reynolds number of target applications require careful assessment of the discretization algorithms on unstructured grids and modelling compromises. High-fidelity simulations with 200-500 million points are not uncommon today and are used to improve scientific understanding of the noise generation process in specific situations. We attempt to discern where the future might take us, especially if exascale computing becomes a reality in 10 years. A pressing question in this context concerns the role of modelling in the coming era. While the sheer scale of the data generated by large-scale simulations will require new methods for data analysis and data visualization, it is our view that suitable theoretical formulations and reduced models will be even more important in future.

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Sparsity-promoting dynamic mode decomposition

Cited by 720 publications

References 42 publications

Dynamic Mode Decomposition with Control

Dynamic Mode Decomposition with Control

Parallel data-driven decomposition algorithm for large-scale datasets: with application to transitional boundary layers

A second golden age of aeroacoustics?

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