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.

翻译：从观测数据中发现控制方程仍是科学建模中的基本挑战，尤其在底层数学结构未知的情况下。传统稀疏辨识方法（如SINDy）虽擅长发现简约模型，但要求研究者预先指定候选基函数，这一局限常导致因关键项遗漏或系统呈现非常规动力学时模型失效。纯符号回归方法虽具有无限灵活性，却易受噪声干扰，常产生过度复杂且不稳定的方程。我们提出AutoSINDy——一种融合符号回归探索能力与SINDy鲁棒稀疏促进特性的"先探索后求解"混合框架。该方法包含三个核心阶段：(1)基于PySR的符号回归从自助抽样数据块中发现候选函数形式；(2)通过共线性分析构建解析管线的分解、扩展与过滤机制，形成最小冗余的综合性函数库；(3)基于定制函数库，SINDy辨识出稀疏控制方程。在典型非线性系统上的大量实验表明：即使在强观测噪声条件下，AutoSINDy仍能稳定恢复真实方程，所有试验中的真实方程恢复率达92.8%。相较于采用增强函数库的标准SINDy及独立符号回归方法，AutoSINDy实现了更高的预测精度、更强的未观测轨迹泛化能力，并显著降低了符号复杂度。