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

arXiv: https://arxiv.org/abs/2603.05201 · HTML: https://mlsanity.com/paper/2603.05201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data](https://mlsanity.com/paper/2009.08810/) (2020)
- [Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling](https://mlsanity.com/paper/2109.05364/) (2021)
- [On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression](https://mlsanity.com/paper/2012.01937/) (2020)
- [Weak-Form Latent Space Dynamics Identification](https://mlsanity.com/paper/2311.12880/) (2023)
- [A toolkit for data-driven discovery of governing equations in high-noise regimes](https://mlsanity.com/paper/2111.04870/) (2021)
- [ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identification](https://mlsanity.com/paper/2410.16528/) (2024)
- [Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inference](https://mlsanity.com/paper/2401.16943/) (2024)
- [Sparse Identification of Nonlinear Dynamics with Conformal Prediction](https://mlsanity.com/paper/2507.11739/) (2025)
- [Some preconditioners for systems of linear inequalities](https://mlsanity.com/paper/1306.5287/) (2013)
- [Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systems](https://mlsanity.com/paper/2509.14219/) (2025)

## Abstract (arXiv)

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.