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

2024/05/14 by Matthew R. Golden, Golden, Matthew · 2 citations
Computer Science · Engineering · #Machine Learning and Data Classification #Fault Detection and Control Systems #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.2405.09579

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.

Cited by

• Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Models
• Data-driven discovery of the equations of turbulent convection

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