摘要: Data-driven discovery of governing equations from time-series data provides a powerful framework for understanding complex biological systems. Library-based approaches that use sparse regression over candidate functions have shown considerable promise, but they face a critical challenge when candidate functions become strongly correlated: numerical ill-conditioning. Poor or restricted sampling, together with particular choices of candidate libraries, can produce strong multicollinearity and numerical instability. In such cases, measurement noise may lead to widely different recovered models, obscuring the true underlying dynamics and hindering accurate system identification. Although sparse regularization promotes parsimonious solutions and can partially mitigate conditioning issues, strong correlations may persist, regularization may bias the recovered models, and the regression problem may remain highly sensitive to small perturbations in the data. We present a systematic analysis of how ill-conditioning affects sparse identification of biological dynamics using benchmark models from systems biology. We show that combinations involving as few as two or three terms can already exhibit strong multicollinearity and extremely large condition numbers. We further show that orthogonal polynomial bases do not consistently resolve ill-conditioning and can perform worse than monomial libraries when the data distribution deviates from the weight function associated with the orthogonal basis. Finally, we demonstrate that when data are sampled from distributions aligned with the appropriate weight functions corresponding to the orthogonal basis, numerical conditioning improves, and orthogonal polynomial bases can yield improved model recovery accuracy across two baseline models. Relevance to Life Sciences Numerical ill-conditioning is especially consequential in the model discovery for biological systems, where nonlinear interactions are often represented using nonlinear functions such as polynomials, and where multiscale dynamics, constrained state trajectories, and limited sampling due to experimental limitations can further amplify multicollinearity. We demonstrate these effects across benchmark models relevant to metabolic networks, regulatory networks, and population dynamics. Our results show that poor conditioning can impair the recovery of biologically meaningful governing equations, while sampling strategies matched to the candidate basis can improve identification accuracy. These results imply that a broader range of dynamic sampling is needed in most biological experiments to produce data sets that are suitable for data-driven model discovery with current methods. Mathematical Content This paper studies sparse regression-based equation discovery in the presence of multicollinearity and numerical ill-conditioning. We analyze the conditioning of candidate libraries, especially monomial and orthogonal polynomial bases, using condition numbers and model recovery under realistic sampling conditions with publicly available experimental data. We compare how basis choice and sampling distribution affect regression stability, sparsity, and the accuracy of recovered dynamical models.