Nonlinear mode decomposition with convolutional neural networks for fluid dynamics

We present a new nonlinear mode decomposition method to visualize decomposed flow fields, named the mode decomposing convolutional neural network autoencoder (MD-CNN-AE). The proposed method is applied to a flow around a circular cylinder at the Reynolds number $Re_{D}=100$ as a test case. The flow...

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Veröffentlicht in:Journal of fluid mechanics Jg. 882
Hauptverfasser: Murata, Takaaki, Fukami, Kai, Fukagata, Koji
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cambridge Cambridge University Press 10.01.2020
Schlagworte:
Activation
Artificial neural networks
Circular cylinders
Computational fluid dynamics
Cylinders
Decomposition
Dimensions
Feature extraction
Fields
Flow mapping
Fluid dynamics
Fluid flow
Fluid mechanics
Hydrodynamics
Machine learning
Methods
Modes
Neural networks
Nonlinear systems
Nonlinearity
Proper Orthogonal Decomposition
Reynolds number
Velocity
ISSN:0022-1120, 1469-7645
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Zusammenfassung:We present a new nonlinear mode decomposition method to visualize decomposed flow fields, named the mode decomposing convolutional neural network autoencoder (MD-CNN-AE). The proposed method is applied to a flow around a circular cylinder at the Reynolds number $Re_{D}=100$ as a test case. The flow attributes are mapped into two modes in the latent space and then these two modes are visualized in the physical space. Because the MD-CNN-AEs with nonlinear activation functions show lower reconstruction errors than the proper orthogonal decomposition (POD), the nonlinearity contained in the activation function is considered the key to improving the capability of the model. It is found by applying POD to each field decomposed using the MD-CNN-AE with hyperbolic tangent activation such that a single nonlinear MD-CNN-AE mode contains multiple orthogonal bases, in contrast to the linear methods, i.e. POD and MD-CNN-AE with linear activation. We further assess the proposed MD-CNN-AE by applying it to a transient process of a circular cylinder wake in order to examine its capability for flows containing high-order spatial modes. The present results suggest a great potential for the nonlinear MD-CNN-AE to be used for feature extraction of flow fields in lower dimensions than POD, while retaining interpretable relationships with the conventional POD modes.
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ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.822