Affiliation:
1. School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen 518055, People's Republic of China
2. Hermann-Föttinger-Institut, Technische Universität Berlin, Müller-Breslau-Straße 8, D-10623 Berlin, Germany
Abstract
We propose a novel trajectory-optimized cluster-based network model (tCNM) for nonlinear model order reduction from time-resolved data following Li et al. [“Cluster-based network model,” J. Fluid Mech. 906, A21 (2021)] and improving the accuracy for a given number of centroids. The starting point is k-means++ clustering, which minimizes the representation error of the snapshots by their closest centroids. The dynamics is presented by “flights” between the centroids. The proposed trajectory-optimized clustering aims to reduce the kinematic representation error further by shifting the centroids closer to the snapshot trajectory and refining state propagation with trajectory support points. Thus, curved trajectories are better resolved. The resulting tCNM is demonstrated for the sphere wake for three flow regimes, including the periodic, quasi-periodic, and chaotic dynamics. The representation error of tCNM is five times smaller as compared to the approximation by the closest centroid. Thus, the error is at the same level as proper orthogonal decomposition (POD) of same order. Yet, tCNM has distinct advantages over POD modeling: it is human interpretable by representing dynamics by a handful of coherent structures and their transitions; it shows robust dynamics by design, i.e., stable long-time behavior; and its development is fully automatable, i.e., it does not require tunable auxiliary closure and other models.
Funder
National Natural Science Foundation of China
Natural Science and Engineering Grant of Guangdong province, China,
Subject
Condensed Matter Physics,Fluid Flow and Transfer Processes,Mechanics of Materials,Computational Mechanics,Mechanical Engineering
Cited by
8 articles.
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