CNN-sindy based reduced order modeling of unsteady flow fields

We present a new framework of nonlinear reduced order model to extract low-dimensional modes and to predict their temporal evolutions. Autoencoder-type Convolutional Neural Network (CNN) which can learn nonlinearity of data is used to extract low-dimensional modes. For obtaining the temporal evolution of a mapped data by CNN, Sparse Identification of Nonlinear Dynamics (SINDy) is performed. The proposed method is applied to a circular cylinder wake at Re_D = 100. The CNN trained using fluctuation components of velocity vector u, v shows better results than the snapshot Proper Orthogonal Decomposition in terms of the energy reconstruction rate. Although time-evolving flow fields reproduced by SINDy equation also show reasonable agreement with the reference direct numerical simulation, the errors of CNN and SINDy are accumulated through integral computation. The error of CNN can be reduced by devising a better network structure; however, the error of SINDy depends on the waveform of latent vector.