mlsanityData to 14 Oct 2026

On the Convergence of the SINDy Algorithm

arXiv 1805.06445 ↗First posted 16 May 2018math.OC cs.IT math.ITcited by 49

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Abstract (arXiv)

One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of parameters which best fits the dynamics while providing the simplest representation (i.e. the smallest amount of terms). One such approach is the sparse identification of nonlinear dynamics framework [6] which uses a sparsity-promoting algorithm that iterates between a partial least-squares fit and a thresholding (sparsity-promoting) step. In this work, we provide some theoretical results on the behavior and convergence of the algorithm proposed in [6]. In particular, we prove that the algorithm approximates local minimizers of an unconstrained ℓ0-penalized least-squares problem. From this, we provide sufficient conditions for general convergence, rate of convergence, and conditions for one-step recovery. Examples illustrate that the rates of convergence are sharp. In addition, our results extend to other algorithms related to the algorithm in [6], and provide theoretical verification to several observed phenomena.

Key facts. Cited by 49 papers in the map (data through 14 Oct 2026). First posted on arXiv 16 May 2018.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 7; 2022: 10; 2023: 6; 2024: 13; 2025: 9; 2026: 4.

49 papers.

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  1. 2021Deeptime: a Python library for machine learning dynamical models from time series datacited by 38
  2. 2021Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approachcited by 36
  3. 2021Learning Mean-Field Equations from Particle Data Using WSINDycited by 29
  4. 2022Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constantscited by 24
  5. 2021DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimizationcited by 19
  6. 2022WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimmingcited by 18
  7. 2021A toolkit for data-driven discovery of governing equations in high-noise regimescited by 15
  8. 2023Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discoverycited by 15
  9. 2023On sparse regression, Lp-regularization, and automated model discoverycited by 15
  10. 2024Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy datacited by 15
  11. 2022Asymptotic consistency of the WSINDy algorithm in the limit of continuum datacited by 14
  12. 2024MODNO: Multi Operator Learning With Distributed Neural Operatorscited by 14
37 more
  1. 2022Online Weak-form Sparse Identification of Partial Differential Equationscited by 13
  2. 2022Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertaintycited by 13
  3. 2022Convergence of weak-SINDy Surrogate Modelscited by 11
  4. 2023Coarse-Graining Hamiltonian Systems Using WSINDycited by 11
  5. 2022Random Feature Models for Learning Interacting Dynamical Systemscited by 10
  6. 2021SHRIMP: Sparser Random Feature Models via Iterative Magnitude Pruningcited by 9
  7. 2024Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inferencecited by 9
  8. 2024Weak-Form Inference for Hybrid Dynamical Systems in Ecologycited by 7
  9. 2024Time-Series Forecasting, Knowledge Distillation, and Refinement within a Multimodal PDE Foundation Modelcited by 7
  10. 2024Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Basescited by 7
  11. 2025Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysiscited by 7
  12. 2023A Robust SINDy Approach by Combining Neural Networks and an Integral Formcited by 6
  13. 2022A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Studycited by 5
  14. 2024Statistical Mechanics of Dynamical System Identificationcited by 5
  15. 2024Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraintcited by 5
  16. 2024Scalable Sparse Regression for Model Discovery: The Fast Lane to Insightcited by 4
  17. 2023Multiphysics discovery with moving boundaries using Ensemble SINDy and Peridynamic Differential Operatorcited by 3
  18. 2024GN-SINDy: Greedy Sampling Neural Network in Sparse Identification of Nonlinear Partial Differential Equationscited by 2
  19. 2024SINDyG: Sparse Identification of Nonlinear Dynamical Systems from Graph-Structured Data, with Applications to Stuart-Landau Oscillator Networkscited by 2
  20. 2025Sparse identification of nonlinear dynamics with library optimization mechanism: Recursive long-term prediction perspectivecited by 2
  21. 2021Uncovering Closed-form Governing Equations of Nonlinear Dynamics from Videoscited by 1
  22. 2022A Symbolic Representation of Human Posture for Interpretable Learning and Reasoningcited by 1
  23. 2025Weighted Birkhoff Averages Accelerate Data-Driven Methodscited by 1
  24. 2026Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regressioncited by 1
  25. 2022A dynamical systems based framework for dimension reductioncited by 0
  26. 2023Dimensionality Collapse: Optimal Measurement Selection for Low-Error Infinite-Horizon Forecastingcited by 0
  27. 2024SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Studycited by 0
  28. 2024Machine learning for cerebral blood vessels' malformationscited by 0
  29. 2025Impilict Runge-Kutta based sparse identification of governing equations in biologically motivated systemscited by 0
  30. 2025BLADE: Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systemscited by 0
  31. 2025Identifying Unknown Stochastic Dynamics via Finite expression methodscited by 0
  32. 2025Optimizing Hard Thresholding for Sparse Model Discoverycited by 0
  33. 2025Sparse Kalman Identification for Partially Observable Systems via Adaptive Bayesian Learningcited by 0
  34. 2025From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identificationcited by 0
  35. 2026Turning mechanistic models into forecasters by using machine learningcited by 0
  36. 2026From Video-to-PDE: Data-Driven Discovery of Nonlinear Dye Plume Dynamicscited by 0
  37. 2026Learning the Geometry of Admissible Hypotheses through Inductive Bias in Training Distributionscited by 0