Towards a data-scale independent regulariser for robust sparse identification of non-linear dynamics
This work is significant for researchers and engineers using sparse regression for system identification, as it makes the process more robust and reliable against data normalization effects, which is a common preprocessing step in real-world applications.
This paper addresses the problem of data normalization distorting sparse identification of non-linear dynamics, particularly in the SINDy framework, leading to dense and incorrect models. The authors introduce Sequential Thresholding of Coefficient of Variation (STCV), a novel sparse regression algorithm that uses a dimensionless statistical metric, Coefficient Presence (CP), instead of magnitude-based thresholding. STCV consistently and significantly outperforms standard methods like STLSQ and E-SINDy on normalized, noisy datasets, successfully identifying correct, sparse physical laws where others fail.
Data normalisation, a common and often necessary preprocessing step in engineering and scientific applications, can severely distort the discovery of governing equations by magnitudebased sparse regression methods. This issue is particularly acute for the Sparse Identification of Nonlinear Dynamics (SINDy) framework, where the core assumption of sparsity is undermined by the interaction between data scaling and measurement noise. The resulting discovered models can be dense, uninterpretable, and physically incorrect. To address this critical vulnerability, we introduce the Sequential Thresholding of Coefficient of Variation (STCV), a novel, computationally efficient sparse regression algorithm that is inherently robust to data scaling. STCV replaces conventional magnitude-based thresholding with a dimensionless statistical metric, the Coefficient Presence (CP), which assesses the statistical validity and consistency of candidate terms in the model library. This shift from magnitude to statistical significance makes the discovery process invariant to arbitrary data scaling. Through comprehensive benchmarking on canonical dynamical systems and practical engineering problems, including a physical mass-spring-damper experiment, we demonstrate that STCV consistently and significantly outperforms standard Sequential Thresholding Least Squares (STLSQ) and Ensemble-SINDy (E-SINDy) on normalised, noisy datasets. The results show that STCV-based methods can successfully identify the correct, sparse physical laws even when other methods fail. By mitigating the distorting effects of normalisation, STCV makes sparse system identification a more reliable and automated tool for real-world applications, thereby enhancing model interpretability and trustworthiness.