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We propose a customized convolutional neural network based autoencoder calleda hierarchical autoencoder, which allows us to extract nonlinear autoencodermodes of flow fields while preserving the contribution order of the latentvectors. As preliminary tests, the proposed method is first applied to acylinder wake at $Re_D$ = 100 and its transient process. It is found that theproposed method can extract the features of these laminar flow fields as thelatent vectors while keeping the order of their energy content. The presenthierarchical autoencoder is further assessed with a two-dimensional $y-z$cross-sectional velocity field of turbulent channel flow at $Re_{\tau}$ = 180in order to examine its applicability to turbulent flows. It is demonstratedthat the turbulent flow field can be efficiently mapped into the latent spaceby utilizing the hierarchical model with a concept of ordered autoencoder modefamily. The present results suggest that the proposed concept can be extendedto meet various demands in fluid dynamics including reduced order modeling andits combination with linear theory-based methods by using its ability toarrange the order of the extracted nonlinear modes.

Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data