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AutoSINDy automates a key step in sparse equation discovery: it uses symbolic regression to propose candidate functional forms, then filters them into a library for SINDy to fit. This reduces the need for researchers to specify basis functions in advance. The reported gains rest on benchmarks across six synthetic nonlinear systems with added noise, so readers should check how well they transfer to messy real-world biological or physical data.
AutoSINDy: Discovery of Nonlinear Dynamics with Automated Library Construction
arXiv:2605.09696v2 Announce Type: replace 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. 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 random subsets of the data; (2) a curation pipeline decomposes, expands, and filters these expressions using collinearity analysis to construct a minimal yet comprehensive library; and (3) the weak form of SINDy identifies sparse governing equations from this custom-tailored library. Extensive experiments across six canonical nonlinear systems, with noise of up to 20% of each variable's standard deviation, demonstrate that AutoSINDy achieves a recovery rate (new-trajectory R^2 > 0.99) of 89.7% across all trials, against at most 45.0% for the baselines, and 67.5% at the highest noise level. Compared with standard SINDy using enriched libraries, its weak form, and standalone symbolic regression, AutoSINDy achieves higher predictive accuracy, superior generalization to unseen trajectories, and equations close to the ground-truth complexity. These results show that AutoSINDy identifies correct governing terms without prior domain knowledge, automating the feature-engineering bottleneck in system identification and offering a pathway for discovering complex dynamics in biological and physical systems where the mathematical form is unknown.
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. 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 random subsets of the data; (2) a curation pipeline decomposes, expands, and filters these expressions using collinearity analysis to construct a minimal yet comprehensive library; and (3) the weak form of SINDy identifies sparse governing equations from this custom-tailored library. Extensive experiments across six canonical nonlinear systems, with noise of up to 20% of each variable's standard deviation, demonstrate that AutoSINDy achieves a recovery rate (new-trajectory R^2 > 0.99) of 89.7% across all trials, against at most 45.0% for the baselines, and 67.5% at the highest noise level. Compared with standard SINDy using enriched libraries, its weak form, and standalone symbolic regression, AutoSINDy achieves higher predictive accuracy, superior generalization to unseen trajectories, and equations close to the ground-truth complexity. These results show that AutoSINDy identifies correct governing terms without prior domain knowledge, automating the feature-engineering bottleneck in system identification and offering a pathway for discovering complex dynamics in biological and physical systems where the mathematical form is unknown.
38 pages, 17 figures. Code available at this https URL
Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE); Symbolic Computation (cs.SC)
I.2.6; G.1.6; J.2
arXiv:2605.09696 [cs.LG]
(or arXiv:2605.09696v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.09696 Focus to learn more arXiv-issued DOI via DataCite
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