Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements

Bright, Ido; Lin, Guang; Kutz, J. Nathan

doi:10.1063/1.4836815

Cited by 171 publications

(135 citation statements)

References 41 publications

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“…ML techniques aim to capitalize on underlying low-dimensional patterns and clustering in data. In the dynamical applications considered here, one might exploit these patterns, or DMD modes, by building libraries of lowrank dynamical modes, much like is done with POD modes [25,26,27]. Such DMD libraries for different dynamical regimes partner nicely with compressive sensing strategies.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Multiresolution Dynamic Mode Decomposition

Kutz

Brunton

2016

SIAM J. Appl. Dyn. Syst.

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342

186

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We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multi-resolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of multi-resolution time-scale components. A one-level separation allows for background (low-rank) and foreground (sparse) separation of dynamical data, or robust principal component analysis. The multi-resolution dynamic mode decomposition is capable of characterizing nonlinear dynamical systems in an equation-free manner by recursively decomposing the state of the system into low-rank terms whose temporal coefficients in time are known. DMD modes with temporal frequencies near the origin (zero-modes) are interpreted as background (low-rank) portions of the given dynamics, and the terms with temporal frequencies bounded away from the origin are their sparse counterparts. The multi-resolution dynamic mode decomposition (mrDMD) method is demonstrated on several examples involving multi-scale dynamical data, showing excellent decomposition results, including sifting the El Niño mode from ocean temperature data. It is further applied to decompose a video data set into separate objects moving at different rates against a slowly varying background. These examples show that the decomposition is an effective dynamical systems tool for data-driven discovery.

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Section: Discussion and Outlookmentioning

confidence: 99%

Multiresolution Dynamic Mode Decomposition

Kutz

Brunton

2016

SIAM J. Appl. Dyn. Syst.

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342

186

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“…27 Similar success has been demonstrated through a combined use of POD, compressive sensing, and supervised learning to determine the Reynolds number associated with numerically simulated cylinder flows from a limited set of surface pressure signals. 28,29 Related techniques have been successful in the context of separated flows for discriminating between actuated and unactuated flows from image data. 30 These latter techniques can potentially be leveraged for wake regime classificationa supervised learning problem aimed at labeling a single snapshot realization of a wake according to an already established library of features and labels, though such a notion is predicated on the availability of a suitable library of wake regime labels and features.…”

Section: Introductionmentioning

confidence: 99%

Learning Wake Regimes from Snapshot Data

Hemati¹

2016

46th AIAA Fluid Dynamics Conference

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Fluid wakes are often categorized by visual inspection according to the number and grouping of vortices shed per cycle (e.g., 2S, 2P, P+S). While such categorizations have proven useful for describing and comparing wakes, the criterion excludes features that are essential to a wake's evolution (i.e., the relative positions and strengths of the shed vortices). For example, not all 2P wakes exhibit the same dynamics; thus, the evolution of wake patterns among 2P wakes can be markedly distinct. Here, we explore the notion of labeling wakes according their dynamics based on empirical snapshot data. Snapshots of the velocity field are reduced to a representative feature vector, which is then processed using machine learning techniques tailored to the task of wake regime learning. The wake regime learning framework is evaluated on an idealized 2P wake model, which can be configured to simulate different (known) dynamical regimes. A simple version of the wake regime learning framework successfully discriminates between dynamically distinct 2P wakes. The results presented here suggest that the wake regime learning perspective may facilitate the development of a new dynamics-based wake labeling convention in the future.

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“…As the Reynolds number increases, additional instabilities develop, resulting in increasingly complex spatial-temporal structures in the wake. Although three-dimensional instabilities typically develop before Re = 1000, this example has been useful for demonstrating sparse sampling strategies in fluid dynamics [5]. The time course of pressures measured at these Reynolds numbers is shown in Figure 3.…”

Section: Examplementioning

confidence: 99%

“…For each regime, the full-state data consisted of 269 pressure measurements collected at 100 time points. Measurements were equally spaced on the surface of the cylinder body as computed by flow simulations described in detail previously [5]. The entire cylinder flow dataset of c = 3 classes consisted of 300 samples at n = 269 measurement locations.…”

Section: Examplementioning

confidence: 99%

“…In this gappy POD technique, a small number of measurements are used to evaluate nonlinear terms in the governing equations and construct POD-Galerkin approximations of complex systems [37]. More recently, the low-rank POD approximations were combined with sparse representation to enable ROM computations with very limited sensors [5,8]. Significant effort has been applied to develop principled, rather than random, sensor placement for ROMs [59,63,15,51].…”

Section: Related Workmentioning

confidence: 99%

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Sparse Sensor Placement Optimization for Classification

Brunton¹,

Brunton²,

Proctor³

et al. 2016

SIAM J. Appl. Math.

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Abstract. Choosing a limited set of sensor locations to characterize or classify a high-dimensional system is an important challenge in engineering design. Traditionally, optimizing the sensor locations involves a brute-force, combinatorial search, which is NP-hard and is computationally intractable for even moderately large problems. Using recent advances in sparsity-promoting techniques, we present a novel algorithm to solve this sparse sensor placement optimization for classification (SSPOC) that exploits low-dimensional structure exhibited by many high-dimensional systems. Our approach is inspired by compressed sensing, a framework that reconstructs data from few measurements. If only classification is required, reconstruction can be circumvented and the measurements needed are orders-of-magnitude fewer still. Our algorithm solves an 1 minimization to find the fewest nonzero entries of the full measurement vector that exactly reconstruct the discriminant vector in feature space; these entries represent sensor locations that best inform the decision task. We demonstrate the SSPOC algorithm on five classification tasks, using datasets from a diverse set of examples, including physical dynamical systems, image recognition, and microarray cancer identification. Once training identifies sensor locations, data taken at these locations forms a low-dimensional measurement space, and we perform computationally efficient classification with accuracy approaching that of classification using full-state data. The algorithm also works when trained on heavily subsampled data, eliminating the need for unrealistic full-state training data.

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Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements

Cited by 171 publications

References 41 publications

Multiresolution Dynamic Mode Decomposition

Multiresolution Dynamic Mode Decomposition

Learning Wake Regimes from Snapshot Data

Sparse Sensor Placement Optimization for Classification

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