Discovery of Nonlinear Dynamics with Automated Basis Function Generation

TL;DR

AutoSINDy is a hybrid framework that combines symbolic regression and sparse identification to discover nonlinear governing equations from noisy data, outperforming traditional methods in accuracy and simplicity.

Contribution

It introduces AutoSINDy, a three-stage hybrid approach that automates basis function generation and robustly identifies equations even with high noise levels.

Findings

AutoSINDy recovers ground-truth equations with 92.8% success rate.

It achieves higher predictive accuracy than standard SINDy and symbolic regression.

AutoSINDy produces simpler, more generalizable models.

Abstract

Discovering governing equations from observational data remains a fundamental challenge in scientific modeling, particularly when the underlying mathematical structure is unknown. Traditional sparse identification methods like SINDy excel at discovering parsimonious models but require researchers to specify candidate basis functions a priori, a limitation that often leads to model failure when critical terms are omitted or when systems exhibit unconventional dynamics. Purely symbolic regression approaches offer unlimited flexibility but struggle with noise sensitivity and frequently produce overly complex, unstable equations. We present AutoSINDy, a hybrid Discovery-then-Solve framework that combines the exploratory power of symbolic regression with the robust sparsity-promoting capabilities of SINDy. Our method operates in three stages: (1) PySR-based symbolic regression discovers candidate functional forms from bootstrapped data chunks; (2) a curation pipeline decomposes, expands, and filters these expressions using collinearity analysis to construct a minimal yet comprehensive library; and (3) SINDy identifies sparse governing equations from this custom-tailored library. Extensive experiments across canonical nonlinear systems demonstrate that AutoSINDy consistently recovers ground-truth equations even under high observational noise, achieving a ground-truth recovery rate of 92.8% across all trials. Compared with standard SINDy using enriched libraries and standalone symbolic regression, AutoSINDy achieves higher predictive accuracy, superior generalization to unseen trajectories, and substantially lower symbolic complexity.