Invertible neural network combined with dynamic mode decomposition applied to flow field feature extraction and prediction

Abstract

The prediction error of the neural network feature extraction methods based on Koopman theory is relatively high due to the non-invertibility of the observable functions. To solve this problem, a novel deep learning architecture named invertible neural network combined with dynamic mode decomposition (INN-DMD) is proposed in this work and is applied to flow field feature extraction and prediction. The INN is used as a vectorized observable function that maps the flow field snapshots from the state space to the latent space. Then, the snapshots on the latent space are decomposed and reconstructed by the DMD algorithm. The proposed method is tested by analyzing the direct simulation results of the flow around a two-dimensional (2D) cylinder at Reynolds number equal to 9×104 and the flow around a 2D NACA (National Advisory Committee for Aeronautics) 0012 airfoil at Reynolds number equal to 2×105. The proposed INN-DMD is also compared to conventional methods such as DMD and Koopman autoencoder combined with DMD (KAE-DMD). Results indicate that INN-DMD predicts the turbulent flow field dataset with greater precision and better stability, using the same number of network parameters, due to its invertibility. INN-DMD is one to two orders of magnitude more accurate than DMD and KAE-DMD using about a quarter of the computational resources, and it shows two orders of magnitude stability improvement compared to the conventional KAE method.