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

## TL;DR

This paper advances methods for discovering dynamical system equations from data by introducing a dual LASSO-based algorithm for improved accuracy and a data-driven library learning approach using STRidge, demonstrated on Lorenz systems.

## Contribution

It presents novel algorithms that enhance the accuracy and stability of sparse regression for dynamical systems and introduces a data-driven method for library construction.

## Key findings

- Dual LASSO improves stability and accuracy.
- Data-driven library learning enhances model interpretability.
- Methods successfully applied to Lorenz systems.

## Abstract

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.