mlsanityData to 14 Oct 2026

Benchmarking sparse system identification with low-dimensional chaos

arXiv 2302.10787 ↗First posted 4 Feb 2023cs.LG cs.SY eess.SYcited by 19

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Abstract (arXiv)

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system identification across scientific domains, but there remains a gap in the literature for large-scale methodological comparisons that are evaluated on a variety of dynamical systems. In this work, we systematically benchmark sparse regression variants by utilizing the dysts standardized database of chaotic systems. In particular, we demonstrate how this open-source tool can be used to quantitatively compare different methods of system identification. To illustrate how this benchmark can be utilized, we perform a large comparison of four algorithms for solving the sparse identification of nonlinear dynamics (SINDy) optimization problem, finding strong performance of the original algorithm and a recent mixed-integer discrete algorithm. In all cases, we used ensembling to improve the noise robustness of SINDy and provide statistical comparisons. In addition, we show very compelling evidence that the weak SINDy formulation provides significant improvements over the traditional method, even on clean data. Lastly, we investigate how Pareto-optimal models generated from SINDy algorithms depend on the properties of the equations, finding that the performance shows no significant dependence on a set of dynamical properties that quantify the amount of chaos, scale separation, degree of nonlinearity, and the syntactic complexity.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). Builds on 50 of its 157 references that are in the map. First posted on arXiv 4 Feb 2023.

Builds on

50 of 157 references.

References · 50

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38 more
  1. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  2. 2019Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systemscited by 96
  3. 2021PySINDy: A comprehensive Python package for robust sparse system identificationcited by 89
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  12. 2018A Unified Framework for Sparse Relaxed Regularized Regression: SR3cited by 36
  13. 2022Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systemscited by 36
  14. 2021Learning Mean-Field Equations from Particle Data Using WSINDycited by 29
  15. 2022Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimizationcited by 29
  16. 2022Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutionscited by 29
  17. 2019Sparse Regression: Scalable algorithms and empirical performancecited by 27
  18. 2022Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifoldscited by 25
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 5; 2024: 4; 2025: 7; 2026: 3.

19 papers.

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  1. 2023Model scale versus domain knowledge in statistical forecasting of chaotic systemscited by 27
  2. 2023Weak-Form Latent Space Dynamics Identificationcited by 20
  3. 2024Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy datacited by 15
  4. 2023Coarse-Graining Hamiltonian Systems Using WSINDycited by 11
  5. 2024ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identificationcited by 11
  6. 2023Detach-ROCKET: Sequential feature selection for time series classification with random convolutional kernelscited by 8
  7. 2025When is a System Discoverable from Data? Discovery Requires Chaoscited by 6
  8. 2024Data-driven local operator finding for reduced-order modelling of plasma systems: I. Concept and verificationscited by 5
  9. 2024Statistical Mechanics of Dynamical System Identificationcited by 5
  10. 2026Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learningcited by 4
  11. 2025Sparse Identification of Nonlinear Dynamics with Conformal Predictioncited by 3
  12. 2026Data-driven discovery of governing differential equations across physical systemscited by 3
7 more
  1. 2025Sparse identification of nonlinear dynamics with library optimization mechanism: Recursive long-term prediction perspectivecited by 2
  2. 2025Data-driven Discovery of Digital Twins in Biomedical Researchcited by 2
  3. 2026The Dynamics of Discoverability: How Trajectories and Priors Shape Equation Recoverycited by 1
  4. 2023System Identification with Copula Entropycited by 0
  5. 2025Impilict Runge-Kutta based sparse identification of governing equations in biologically motivated systemscited by 0
  6. 2025A tensor network approach for chaotic time series predictioncited by 0
  7. 2025SINDy on slow manifoldscited by 0