Scalable Sparse Regression for Model Discovery: The Fast Lane to Insight
This work addresses the computational bottleneck in model discovery for dynamical systems, offering a scalable solution for researchers in fields like physics and engineering, though it is incremental as it builds on existing sparse regression methods.
The authors tackled the problem of learning governing equations from data using sparse regression on symbolic libraries, which was computationally prohibitive for large libraries. They introduced SPRINT, an accelerated algorithm that reduces the computation time from an exhaustive search taking the age of the universe to just a day.
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.