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

arXiv: https://arxiv.org/abs/2405.09579 · HTML: https://mlsanity.com/paper/2405.09579/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 32 references that are in the map.
- First posted on arXiv 14 May 2024.

## Builds on (most cited first, 3 of 3)

- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [On the Convergence of the SINDy Algorithm](https://mlsanity.com/paper/1805.06445/) (2018)

## Built on by (most cited first, 4 of 4)

- [The Weak Form Is Stronger Than You Think](https://mlsanity.com/paper/2409.06751/) (2024)
- [Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Models](https://mlsanity.com/paper/2509.03036/) (2025)
- [Impilict Runge-Kutta based sparse identification of governing equations in biologically motivated systems](https://mlsanity.com/paper/2502.20319/) (2025)
- [Balance-Guided Sparse Identification of Multiscale Nonlinear PDEs with Small-coefficient Terms](https://mlsanity.com/paper/2604.18414/) (2026)

## Abstract (arXiv)

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.