Data driven discovery of nonlinear dynamics

We demonstrate that sparse regression and compressive sensing techniques are capable of accurately determining a set of functions governing a nonlinear dynamical system. We analyze a technique introduced by Brunton, Proctor, and Kutz, 2016 [1] that builds a sparse representation of a dynamical system by computing sequential least squares fittings of the data to identify the governing equations. By computing the sparse regression in such a fashion, this method quickly identifies nonzero coefficients and allows them to converge to their respective weight. The result is a sparse representation of the dynamical system in the nonlinear function space. We look at the mechanics of the lasso, discuss the introduction of sparsity to a system by choice of the l1-norm, and investigate the algorithm used in sparse identification of nonlinear dynamics through a sequential least squares method.