Collinearity-Resilient Sparse Identification of Nonlinear Dynamics via Cluster-Stability and Representative Selection

Sparse identification of nonlinear dynamics (SINDy) exhibit structural fragilely when the candidate library contains highly correlated functions, as standard feature-wise selection tends to scatter selection frequencies across near-multicollinear terms and can therefore omit truly active variables. To overcome this limitation, in this paper, we propose a collinearity-aware SINDy framework that groups correlated candidates, evaluates cluster-level stability over repeated sparse-regression fits, and disambiguates each retained group by selecting a unique representative through independent-trajectory validation, followed by coefficient re-estimation on the fixed support. Experiments show that the proposed cluster-level approach achieves 85.0% exact recovery at a derivative-perturbation level of 0.30, compared with 67.7% for tuned STRidge and 35.3% for tuned feature-wise stability selection. Its applicability is further validated on a damped nonlinear pendulum, where 100.0% system-level exact recovery was achieved for the highly correlated terms $\theta$ and $\sin \theta$. Collectively, these results demonstrate that cluster-level stability and independent-trajectory disambiguation can improve the structural recovery in highly collinear candidate libraries.