Sparse Regression and Adaptive Feature Generation for the Discovery of Dynamical Systems

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data, proposed by Brunton et al., followed by performance of LASSO for this purpose. We then propose a new algorithm that uses the dual of LASSO optimization for higher accuracy and stability. In the second part, we propose a novel algorithm that learns the candidate function library in a completely data-driven manner to distill the governing equations of the dynamical system. This is achieved via sequentially thresholded ridge regression (STRidge) over a orthogonal polynomial space. The performance of the three discussed methods is illustrated by looking the Lorenz 63 system and the quadratic Lorenz system.