Deep learning method for identifying the minimal representations and nonlinear mode decomposition of fluid flows

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We propose a deep learning method to learn the minimal representations of fluid flows. It uses the deep variational autoencoder (VAE) to decouple the independent representations for fluid flows. We apply this method to several simple flows and show that the network successfully identifies the independent and interpretable representations. It shows that the proposed method can extract the physically suggestive information. We further employ the VAE network to improve the mode decomposing autoencoder framework. It decomposes the cylinder flow fields into two independent ordered states. The cylinder flow at different Reynolds numbers and time can be described as the composition of the two decomposed fields. The present results suggest that the proposed network can be used as an effective nonlinear dimensionality reduction tool for flow fields.