Low-Dimensional Dynamic Representation of Unsteady Flow Using Convolutional Neural Network

To obtain low-dimensional dynamic representation and spatio-temporal mode decompositions of unsteady flow, we develop 3D-CNN Mode Decomposition Model. The model is applied to flow around a cylinder at Reynolds number, \({Re}_{D}={U}_{\infty }D/\nu\) =100, as an example of unsteady flows. The input of the model, which is a time series of flow field during one cycle of vortex shedding, are mapped into 3 modes in the latent space, and then a time series of each decomposed flow field is reconstructed from each mode. For low-dimensional dynamic representation, the models with only 3 modes can represent the flow field for one cycle of vortex shedding with high accuracy. For spatio-temporal mode decompositions, the first decomposed field, which has largest energy, shows large unsteady structures, corresponding to the Karman vortices in the wake region. The second decomposed flow fields is similar to the time-averaged flow fields of the ground truth with small and higher frequency oscillations. The third decomposed field, which has smallest energy, consists of unsteady structures of opposite phase, smaller size, and smaller magnitude in the wake. By developing 3D-CNN-MD Model, we can enhance our understanding of the flow fields with spatio-temporal variations though deep learning.