mlsanityData to 7 Oct 2026

Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling

arXiv 2109.05364 ↗First posted 11 Sep 2021cs.LG physics.comp-phcited by 27

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Abstract (arXiv)

Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability guarantees. We present here a unification of the Sparse Identification of Nonlinear Dynamics (SINDy) formalism with neural ordinary differential equations. The resulting framework allows learning of both "black-box" dynamics and learning of structure preserving bracket formalisms for both reversible and irreversible dynamics. We present a suite of benchmarks demonstrating effectiveness and structure preservation, including for chaotic systems.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 25 of its 58 references that are in the map. First posted on arXiv 11 Sep 2021.

Builds on

25 of 58 references.

References · 25

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13 more
  1. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 77
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 4; 2023: 6; 2024: 4; 2025: 7; 2026: 6.

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  1. 2023Correcting model misspecification in physics-informed neural networks (PINNs)cited by 33
  2. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  3. 2022Interpretable Polynomial Neural Ordinary Differential Equationscited by 24
  4. 2024Efficiently Parameterized Neural Metriplectic Systemscited by 18
  5. 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 17
  6. 2024Symmetry-Informed Governing Equation Discoverycited by 14
  7. 2024Learning Physics From Video: Unsupervised Physical Parameter Estimation for Continuous Dynamical Systemscited by 13
  8. 2026Think like a Scientist: Physics-guided LLM Agent for Equation Discoverycited by 13
  9. 2023Coarse-Graining Hamiltonian Systems Using WSINDycited by 11
  10. 2023AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regressioncited by 9
  11. 2025Discovering Symbolic Differential Equations with Symmetry Invariantscited by 6
  12. 2024Generalizing the SINDy approach with nested neural networkscited by 2
15 more
  1. 2025Equilibrium Conserving Neural Operators for Super-Resolution Learningcited by 2
  2. 2025Meta-learning Structure-Preserving Dynamicscited by 2
  3. 2025Data-driven Discovery of Digital Twins in Biomedical Researchcited by 2
  4. 2025Neural non-canonical Hamiltonian dynamics for long-time simulationscited by 2
  5. 2022Mining Causality from Continuous-time Dynamics Models: An Application to Tsunami Forecastingcited by 1
  6. 2023Pseudo-Hamiltonian system identificationcited by 1
  7. 2023Interpretable Neural PDE Solvers using Symbolic Frameworkscited by 1
  8. 2025Function Spaces Without Kernels: Learning Compact Hilbert Space Representationscited by 1
  9. 2025Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurementscited by 1
  10. 2022Parameter-varying neural ordinary differential equations with partition-of-unity networkscited by 0
  11. 2026Towards a data-scale independent regulariser for robust sparse identification of non-linear dynamicscited by 0
  12. 2026From Data to Laws: Neural Discovery of Conservation Laws Without False Positivescited by 0
  13. 2026AC-SINDy: Compositional Sparse Identification of Nonlinear Dynamicscited by 0
  14. 2026Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamicscited by 0
  15. 2026Data-Driven Learning of Unknown Nonlinear Differential Equations Using Functional Analysiscited by 0