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Abstract
Dynamic Mode Decomposition (DMD) techniques have risen as prominent feature identification methods in the field of fluid dynamics. Any of the multiple variables of the DMD method allows to identify meaningful features from either experimental or numerical flow data on a data-driven manner. Performing a DMD analysis requires handling matrices V ∈ R n p × N , where n p and N are indicative of the spatial and temporal resolutions. The DMD analysis of a complex flow field requires long temporal sequences of well resolved data, and thus the memory footprint may become prohibitively large. In this contribution, the effect that principled spatial agglomeration (i.e., reduction in n p via clustering) has on the results derived from the DMD analysis is investigated. We compare twelve different clustering algorithms on three testcases, encompassing different flow regimes: a synthetic flow field, a R e D = 60 flow around a cylinder cross section, and a R e τ ≈ 200 turbulent channel flow. The performance of the clustering techniques is thoroughly assessed concerning both the accuracy of the results retrieved and the computational performance. From this assessment, we identify DBSCAN/HDBSCAN as the methods to be used if only relatively high agglomeration levels are affordable. On the contrary, Mini-batch K-means arises as the method of choice whenever high agglomeration n p ˜ / n p ≪ 1 is possible.
Highlights
The characterization of complex flow phenomena is typically attained by resorting to experimental (Laser Doppler Anemometry, Particle Image Velocimetry, . . . ) and/or numerical (Computational FluidDynamics simulations) tools
In Reference [30], the spatial reduction was attained via the application of the K-means algorithm. In this contribution we explore a possible avenue to alleviate the computational cost associated to the data-driven Dynamic Mode Decomposition (DMD) analysis of complex flow fields: following Reference [30], we investigate how the principled reduction of the data matrix using different unsupervised learning algorithms affects the quality of the results that DMD can obtain
The first testcase pertains to a one-dimensional field with spatio-temporal dependence. This flow is very useful as it provides a good example of why reducing the input data matrix along its leading dimension is potentially more profitable than reducing it along its second dimension. This testcase will allow us to establish a metrics allowing a fair comparison of the different spatial agglomeration techniques considered
Summary
The characterization of complex flow phenomena is typically attained by resorting to experimental (Laser Doppler Anemometry, Particle Image Velocimetry, . . . ) and/or numerical (Computational FluidDynamics simulations) tools. The characterization of complex flow phenomena is typically attained by resorting to experimental Perhaps the most common strategies are the Proper. Orthogonal Decomposition (POD) and the Dynamic Mode Decomposition (DMD) techniques. Proper Orthogonal Decomposition techniques, ([1,2,3,4])— known as Principal Component. Analysis or Karhunen-Loève decomposition– operate on sequences of snapshots, that is, either experimental measurements or numerical solutions acquired at successive time instants. An optimal representation of the sequence is provided by the POD method, as features identified by POD are orthogonal to each other [4]. Techniques to perform Spectral POD have been described in References [5,6,7]
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