Towards a data-scale independent regulariser for robust sparse identification of non-linear dynamics

Abstract

Data normalisation, a common, often necessary preprocessing step in engineering and scientific applications, can severely distort the discovery of governing equations by magnitude-based sparse regression methods. This is particularly acute for the Sparse Identification of Nonlinear Dynamics (SINDy) framework, where the core sparsity assumption is undermined by the interaction between data scaling and measurement noise, yielding dense, uninterpretable, physically incorrect models. To address this vulnerability, we introduce Sequential Thresholding of Coefficient of Variation (STCV), a novel, computationally efficient sparse regression algorithm 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 library terms. This shift from magnitude to statistical significance makes term selection largely insensitive to arbitrary per-variable scaling. We say “largely insensitive” rather than “invariant” because STCV’s inner loop still relies on a Sequentially Thresholded Least Squares (STLSQ) step with a small fixed near-zero threshold; this step is magnitude-dependent and can in principle retain residual scale sensitivity, though in practice the dimensionless CP metric dominates selection, as shown empirically in Section 4 . Through comprehensive benchmarking on canonical dynamical systems and practical engineering problems, including a physical mass–spring–damper experiment, we demonstrate STCV consistently and significantly outperforms standard STLSQ and Ensemble-SINDy (E-SINDy) on normalised, noisy datasets, identifying 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, enhancing model interpretability and trustworthiness.