Constrained LASSO for Sparse Identification of Nonlinear Dynamical Systems (SINDy)

Abstract

Our work explores and expands on (Brunton, Proctor, and Kutz, 2016) with regard to bluff body vortex shedding. We have adapted the SINDy method by applying a transformation of the data to reduce the number of dimensions under investigation. We also applied Galerkin constraints associated with our transformation in order to further reduce the variables being considered when model building. Finally, by using LASSO as our method of solving the SINDy problem rather than sequential threshold least squares, we have created a much more efficient approach that attempts to discover the generating equations of the non-linear dynamical system associated with vortex shedding in the wake of a flat plate. Our approach was tested by modeling vortex shedding in the wake of a cylindrical bluff body with a low Reynolds number, and was able to extract expected elements of the governing equations. With this success, we established several models for vortex shedding in the wake of a flat plate bluff body (for both open and closed ends) at a high Reynolds number. Under our transformed data, we obtained 2, 3 and 5 mode models that may shed some light into the dynamics of the system.