mlsanityData to 14 Oct 2026

Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

arXiv 1909.10638 ↗First posted 23 Sep 2019math.DS stat.MLcited by 85

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Abstract (arXiv)

We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of high-dimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems.

Key facts. Cited by 85 papers in the map (data through 14 Oct 2026). First posted on arXiv 23 Sep 2019.

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Citing papers per year: 2021: 15; 2022: 8; 2023: 14; 2024: 17; 2025: 14; 2026: 17.

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  1. 2021Modern Koopman Theory for Dynamical Systemscited by 276
  2. 2021Convergence Rates for Learning Linear Operators from Noisy Datacited by 55
  3. 2023Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEscited by 49
  4. 2021Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systemscited by 45
  5. 2021Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learningcited by 39
  6. 2021Deeptime: a Python library for machine learning dynamical models from time series datacited by 38
  7. 2022Residual Dynamic Mode Decomposition: Robust and verified Koopmanismcited by 36
  8. 2021Learning the temporal evolution of multivariate densities via normalizing flowscited by 18
  9. 2022One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernelscited by 15
  10. 2023Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systemscited by 15
  11. 2021Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Seriescited by 14
  12. 2023Mori-Zwanzig latent space Koopman closure for nonlinear autoencodercited by 12
38 more
  1. 2024Koopman-Assisted Reinforcement Learningcited by 11
  2. 2023Neural Koopman prior for data assimilationcited by 10
  3. 2024Adversarial dynamical systems characterize when data-driven learning succeeds or failscited by 10
  4. 2021Learning the Koopman Eigendecomposition: A Diffeomorphic Approachcited by 9
  5. 2024Dynamical systems and complex networks: A Koopman operator perspectivecited by 9
  6. 2024Learning the Infinitesimal Generator of Stochastic Diffusion Processescited by 9
  7. 2021Extracting stochastic dynamical systems with α-stable L'evy noise from datacited by 8
  8. 2021Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systemscited by 7
  9. 2022An end-to-end deep learning approach for extracting stochastic dynamical systems with α-stable L'evy noisecited by 7
  10. 2024Laplace Transform Based Low-Complexity Learning of Continuous Markov Semigroupscited by 7
  11. 2021Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulascited by 6
  12. 2022Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectoriescited by 6
  13. 2023Equivariance and partial observations in Koopman operator theory for partial differential equationscited by 6
  14. 2024From Biased to Unbiased Dynamics: An Infinitesimal Generator Approachcited by 6
  15. 2021On the Universal Transformation of Data-Driven Models to Control Systemscited by 5
  16. 2021Generalizing Dynamic Mode Decomposition: Balancing Accuracy and Expressiveness in Koopman Approximationscited by 5
  17. 2023Kernelized Diffusion mapscited by 5
  18. 2024Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operatorcited by 5
  19. 2024Kernel Sum of Squares for Data Adapted Kernel Learning of Dynamical Systems from Data: A global optimization approachcited by 4
  20. 2024Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order modelscited by 4
  21. 2023Transfer operators on graphs: Spectral clustering and beyondcited by 3
  22. 2023Online Infinite-Dimensional Regression: Learning Linear Operatorscited by 3
  23. 2023Bridging Algorithmic Information Theory and Machine Learning: A New Approach to Kernel Learningcited by 3
  24. 2024Physics-informed AI and ML-based sparse system identification algorithm for discovery of PDE's representing nonlinear dynamic systemscited by 3
  25. 2024Learning dynamical systems from data: Gradient-based dictionary optimizationcited by 3
  26. 2024On the relationship between Koopman operator approximations and neural ordinary differential equations for data-driven time-evolution predictionscited by 3
  27. 2025Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoderscited by 3
  28. 2021Efficient time stepping for numerical integration using reinforcement learningcited by 2
  29. 2023Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimizationcited by 2
  30. 2023Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systemscited by 2
  31. 2024On the Convergence of Hermitian Dynamic Mode Decompositioncited by 2
  32. 2025Koopman Eigenfunction-Based Identification and Optimal Nonlinear Control of Turbojet Enginecited by 2
  33. 2025From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemmacited by 2
  34. 2025How deep is your network? Deep vs. shallow learning of transfer operatorscited by 2
  35. 2021Data-driven modelling of nonlinear dynamics by barycentric coordinates and memorycited by 1
  36. 2022Towards Data-driven LQR with Koopmanizing Flowscited by 1
  37. 2022Ensemble forecasts in reproducing kernel Hilbert space familycited by 1
  38. 2022Likelihood-based generalization of Markov parameter estimation and multiple shooting objectives in system identificationcited by 1

50 most cited of 85 All 85 (JSON)