Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. first apply the SINDy with two regression methods, thresholded least square algorithm and adaptive absolute shrinkage selection operator which show reasonable ability wide range sparsity constant in our preliminary tests, to two-dimensional single cylinder wake at $Re_D=100$ , its transient process two-parallel cylinders, as examples high-dimensional fluid data. To handle these data whose library matrix is suitable low-dimensional variable combinations, convolutional neural network-based autoencoder (CNN-AE) utilized. The CNN-AE employed map into latent space. then seeks governing equation mapped vector. Temporal evolution can be provided by combining predicted vector CNN decoder remap original dimension. provide stable solution CNN-SINDy-based modelling reproduce fields successfully, although more terms are required represent than periodic shedding. A nine-equation turbulent shear model finally considered examine applicability turbulence, without using CNN-AE. present results suggest that proposed scheme an appropriate parameter choice enables us analyse interpretable manifolds.