  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.
