Nonlinear mode decomposition with convolutional neural networks for fluid dynamics

Abstract

We present a new nonlinear mode decomposition method to visualize the\ndecomposed flow fields, named the mode decomposing convolutional neural network\nautoencoder (MD-CNN-AE). The proposed method is applied to a flow around a\ncircular cylinder at $Re_D=100$ as a test case. The flow attributes are mapped\ninto two modes in the latent space and then these two modes are visualized in\nthe physical space. Because the MD-CNN-AEs with nonlinear activation functions\nshow lower reconstruction errors than the proper orthogonal decomposition\n(POD), the nonlinearity contained in the activation function is considered the\nkey to improve the capability of the model. It is found by applying POD to each\nfield decomposed using the MD-CNN-AE with hyperbolic tangent activation that a\nsingle nonlinear MD-CNN-AE mode contains multiple orthogonal bases, in contrast\nto the linear methods, i.e., POD and the MD-CNN-AE with linear activation. We\nfurther assess the proposed MD-CNN-AE by applying it to a transient process of\na circular cylinder wake in order to examine its capability for flows\ncontaining high-order spatial modes. The present results suggest a great\npotential for the nonlinear MD-CNN-AE to be used for feature extraction of flow\nfields in lower dimension than POD, while retaining interpretable relationships\nwith the conventional POD modes.\n