Scalable Sparse Regression for Model Discovery: The Fast Lane to Insight

TL;DR

This paper introduces SPRINT, a scalable sparse regression algorithm that efficiently discovers governing equations from large datasets, significantly reducing computational time compared to exhaustive search methods.

Contribution

The paper presents SPRINT, a novel, model-agnostic sparse regression algorithm that accelerates equation discovery using iterative SVD and analytic bounds, enabling practical analysis of large symbolic libraries.

Findings

Achieves equation discovery in a day that would take an age with exhaustive search.

Maintains sensitivity to small coefficients in large symbolic libraries.

Reduces computational cost dramatically compared to traditional methods.

Abstract

There exist endless examples of dynamical systems with vast available data and unsatisfying mathematical descriptions. Sparse regression applied to symbolic libraries has quickly emerged as a powerful tool for learning governing equations directly from data; these learned equations balance quantitative accuracy with qualitative simplicity and human interpretability. Here, I present a general purpose, model agnostic sparse regression algorithm that extends a recently proposed exhaustive search leveraging iterative Singular Value Decompositions (SVD). This accelerated scheme, Scalable Pruning for Rapid Identification of Null vecTors (SPRINT), uses bisection with analytic bounds to quickly identify optimal rank-1 modifications to null vectors. It is intended to maintain sensitivity to small coefficients and be of reasonable computational cost for large symbolic libraries. A calculation that would take the age of the universe with an exhaustive search but can be achieved in a day with SPRINT.