mlsanityData to 14 Oct 2026

Sparse identification of nonlinear dynamics with library optimization mechanism: Recursive long-term prediction perspective

arXiv 2507.18220 ↗First posted 24 Jul 2025cs.LG math.DScited by 2

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Abstract (arXiv)

The sparse identification of nonlinear dynamics (SINDy) approach can discover the governing equations of dynamical systems based on measurement data, where the dynamical model is identified as the sparse linear combination of the given basis functions. A major challenge in SINDy is the design of a library, which is a set of candidate basis functions, as the appropriate library is not trivial for many dynamical systems. To overcome this difficulty, this study proposes SINDy with library optimization mechanism (SINDy-LOM), which is a combination of the sparse regression technique and the novel learning strategy of the library. In the proposed approach, the basis functions are parametrized. The SINDy-LOM approach involves a two-layer optimization architecture: the inner-layer, in which the data-driven model is extracted as the sparse linear combination of the candidate basis functions, and the outer-layer, in which the basis functions are optimized from the viewpoint of the recursive long-term (RLT) prediction accuracy; thus, the library design is reformulated as the optimization of the parametrized basis functions. The dynamical model obtained by SINDy-LOM has good interpretability and usability, as this approach yields a parsimonious closed-form model. The library optimization mechanism significantly reduces user burden. The RLT perspective improves the reliability of the resulting model compared with the traditional SINDy approach that can only ensure the one-step-ahead prediction accuracy. The effectiveness of the proposed approach is verified through numerical experiments.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 21 of its 71 references that are in the map. First posted on arXiv 24 Jul 2025.

Builds on

21 of 71 references.

References · 21

  1. 2020Weak SINDy For Partial Differential Equationscited by 155
  2. 2017Sparse identification of nonlinear dynamics for model predictive control in the low-data limitcited by 140
  3. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 137
  4. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  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. 2021Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approachcited by 36
  8. 2024SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learningcited by 26
  9. 2023Benchmarking sparse system identification with low-dimensional chaoscited by 19
  10. 2024ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identificationcited by 11
  11. 2020Prediction with Approximated Gaussian Process Dynamical Modelscited by 8
  12. 2023Learning Parametric Koopman Decompositions for Prediction and Controlcited by 6
9 more
  1. 2022An Online Data-Driven Method to Locate Forced Oscillation Sources from Power Plants Based on Sparse Identification of Nonlinear Dynamics (SINDy)cited by 5
  2. 2021Learning-based Event-triggered MPC with Gaussian processes under terminal constraintscited by 2
  3. 2023Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI)cited by 2
  4. 2024Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flowscited by 2
  5. 2023Practical one-shot data-driven design of fractional-order PID controller: Fictitious reference signal approachcited by 1
  6. 2024Simple controller design to achieve iso-damping robustness: Non-iterative data-driven approach based on fractional-order reference modelcited by 1
  7. 2024Data-driven discovery of mechanical models directly from MRI spectral datacited by 1
  8. 2025Sparse Identification of Nonlinear Dynamics Enhanced by Ensemble Learning, Multi-Step Prediction Evaluation, Elite Strategy, and Classification Techniques for Applications to Industrial Systemscited by 1
  9. 2025Fractional-order controller tuning via minimization of integral of time-weighted absolute error without multiple closed-loop testscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learningcited by 4
  2. 2026AC-SINDy: Compositional Sparse Identification of Nonlinear Dynamicscited by 0