Orthogonal constrained flow time history autoencoder for temporal reduction and mode decomposition

Autoencoder (AE) has shown promising potential for flow modal analysis. However, the flow decomposition mechanism and model interpretability of AE remain open, and deep learning of flow time history (FTH) data for a temporal reduction may help to further improve this. In this study, orthogonal constraints are added on FTH-AE aiming to decompose the flow system into disentangled and explainable flow modes. The FTH-AE first compresses the FTH samples at each position into a low-dimensional latent code, and the codes at all positions are then reconstructed back to FTH data. Meanwhile, orthogonal constraints are imposed to the nonlinear encoder output, linear encoder output, and decoder output to constrain the learned features. Laminar and turbulent flow cases indicate that the orthogonality constrained FTH-AEs are interpretable deep learning models. The code of each FTH sample represents the weight of the fundamental temporal features at that particular flow position, while the distribution of the code represents the corresponding spatial mode. The turbulence results also indicate that the proposed method provides a more accurate reconstruction result than conventional linear theory-based methods. The orthogonal constrained FTH-AE models are much more straightforward yet more flexible than variational autoencoders. This is an alternative deep learning approach to learn the disentangled flow knowledge directly from the raw FTH data.