Nonlinear Mode Decomposition Via Physics-Assimilated Convolutional Autoencoder for Unsteady Flows over an Airfoil

I have developed a physics-assimilated convolutional autoencoder (CAE) neural network, namely, PhyAENet, to carry out nonlinear mode decomposition of the unsteady flow field around a National Advisory Committee for Aeronautics 4412 airfoil near stall conditions. The flow field snapshots are mapped into latent modes by the encoder part of the well-trained CAE, which are used for dynamic mode decomposition (DMD) analysis. The computed DMD modes are split into modes covering different frequency ranges. These high and low-frequency DMD modes are used to form reconstructed encoded sequences, which are then mapped back to generate the nonlinear decomposed spatiotemporal modes by the decoder of the CAE. As such, physics is assimilated into the neural network by incorporating the frequencies of the DMD modes into the latent modes in the latent space. The proposed PhyAENet is capable of extracting the dominant features of the flow fields, accounting for the nonlinearity of the underlying dynamics. Furthermore, the extracted nonlinear modes are evolving with time and physically interpretable. It is revealed that the nonlinear modes can be well represented when using more DMD modes for reconstruction of the encoded sequences. The energy spectrum of the nonlinear modes are obtained by ranking the Frobenius norm of the mode vector.