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From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identification

arXiv 2512.14404 ↗First posted 16 Dec 2025stat.ML cs.LG math.OCcited by 0

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Abstract (arXiv)

In this work, we revisit dictionary-based sparse regression, in particular, Sequential Threshold Least Squares (STLS), and propose a score-guided library selection to provide practical guidance for data-driven modeling, with emphasis on SINDy-type algorithms. STLS is an algorithm to solve the ℓ0 sparse least-squares problem, which relies on splitting to efficiently solve the least-squares portion while handling the sparse term via proximal methods. It produces coefficient vectors whose components depend on both the projected reconstruction errors, here referred to as the scores, and the mutual coherence of dictionary terms. The first contribution of this work is a theoretical analysis of the score and dictionary-selection strategy. This could be understood in both the original and weak SINDy regime. Second, numerical experiments on ordinary and partial differential equations highlight the effectiveness of score-based screening, improving both accuracy and interpretability in dynamical system identification. These results suggest that integrating score-guided methods to refine the dictionary more accurately may help SINDy users in some cases to enhance their robustness for data-driven discovery of governing equations.

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References · 22

  1. 2020Weak SINDy For Partial Differential Equationscited by 155
  2. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 137
  3. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  4. 2017Sparse learning of stochastic dynamic equationscited by 76
  5. 2018On the Convergence of the SINDy Algorithmcited by 49
  6. 2019A unified sparse optimization framework to learn parsimonious physics-informed models from datacited by 49
  7. 2018A Unified Framework for Sparse Relaxed Regularized Regression: SR3cited by 36
  8. 2021Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approachcited by 36
  9. 2015False Discoveries Occur Early on the Lasso Pathcited by 31
  10. 2024SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learningcited by 26
  11. 2020SINDy-BVP: Sparse Identification of Nonlinear Dynamics for Boundary Value Problemscited by 22
  12. 2021SINDy with Control: A Tutorialcited by 15
10 more
  1. 2023Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discoverycited by 15
  2. 2024Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy datacited by 15
  3. 2022Convergence of weak-SINDy Surrogate Modelscited by 11
  4. 2024The Weak Form Is Stronger Than You Thinkcited by 11
  5. 2024ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identificationcited by 11
  6. 2022Simultaneous Identification and Denoising of Dynamical Systemscited by 10
  7. 2023HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equationscited by 8
  8. 2023Streaming Compression of Scientific Data via weak-SINDycited by 6
  9. 2024Statistical Mechanics of Dynamical System Identificationcited by 5
  10. 2023Scalable variable selection for two-view learning tasks with projection operatorscited by 1

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