Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

Understand

We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena.

• We first apply the SINDy with two regression methods, the thresholded least square algorithm (TLSA) and the adaptive Lasso (Alasso) which show reasonable ability with a wide range of sparsity constant in our preliminary tests, to a two-dimensional single cylinder wake at $Re_D=100$, its transient process, and a wake of two-parallel cylinders, as examples of high-dimensional fluid data.
• To handle these high dimensional data with SINDy whose library matrix is suitable for low-dimensional variable combinations, a convolutional neural network-based autoencoder (CNN-AE) is utilized.
• The CNN-AE is employed to map a high-dimensional dynamics into a low-dimensional latent space.