mlsanityData to 7 Oct 2026

Koopman Operator Dynamical Models: Learning, Analysis and Control

arXiv 2102.02522 ↗First posted 4 Feb 2021eess.SY cs.SY math.DScited by 42

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Abstract (arXiv)

The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework. Although there are principled ways of learning such finite approximations, they are in many instances overlooked in favor of, often ill-posed and unstructured methods. Also, Koopman operator theory has long-standing connections to known system-theoretic and dynamical system notions that are not universally recognized. Given the former and latter realities, this work aims to bridge the gap between various concepts regarding both theory and tractable realizations. Firstly, we review data-driven representations (both unstructured and structured) for Koopman operator dynamical models, categorizing various existing methodologies and highlighting their differences. Furthermore, we provide concise insight into the paradigm's relation to system-theoretic notions and analyze the prospect of using the paradigm for modeling control systems. Additionally, we outline the current challenges and comment on future perspectives.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Feb 2021.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 3; 2023: 6; 2024: 10; 2025: 11; 2026: 10.

42 papers.

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  1. 2023Koopman Kernel Regressioncited by 22
  2. 2022Unsupervised Learning of Equivariant Structure from Sequencescited by 15
  3. 2021Diffeomorphically Learning Stable Koopman Operatorscited by 13
  4. 2021Learning the Koopman Eigendecomposition: A Diffeomorphic Approachcited by 9
  5. 2024Dynamical systems and complex networks: A Koopman operator perspectivecited by 9
  6. 2025Latent Mamba Operator for Partial Differential Equationscited by 8
  7. 2024Nonparametric Control Koopman Operatorscited by 7
  8. 2025Koopman-Equivariant Gaussian Processescited by 6
  9. 2025Modeling Partially Observed Nonlinear Dynamical Systems and Efficient Data Assimilation via Discrete-Time Conditional Gaussian Koopman Networkcited by 6
  10. 2023On the lifting and reconstruction of nonlinear systems with multiple invariant setscited by 4
  11. 2024SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systemscited by 4
  12. 2023Easy attention: A simple attention mechanism for temporal predictions with transformerscited by 3
30 more
  1. 2024CoNO: Complex Neural Operator for Continous Dynamical Physical Systemscited by 3
  2. 2024Linear quadratic control of nonlinear systems with Koopman operator learning and the Nystr"om methodcited by 2
  3. 2025Koopman Eigenfunction-Based Identification and Optimal Nonlinear Control of Turbojet Enginecited by 2
  4. 2025GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equationscited by 2
  5. 2025From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemmacited by 2
  6. 2022Towards Data-driven LQR with Koopmanizing Flowscited by 1
  7. 2022Ensemble forecasts in reproducing kernel Hilbert space familycited by 1
  8. 2023Joint Problems in Learning Multiple Dynamical Systemscited by 1
  9. 2024Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMDcited by 1
  10. 2024Spectrally Informed Learning of Fluid Flowscited by 1
  11. 2024End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic datacited by 1
  12. 2024Kernel-Based Optimal Control: An Infinitesimal Generator Approachcited by 1
  13. 2025Data-driven system identification using quadratic embeddings of nonlinear dynamicscited by 1
  14. 2025Understanding the role of autoencoders for stiff dynamical systems using information theorycited by 1
  15. 2025SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecastingcited by 1
  16. 2026HyCOP: Hybrid Composition Operators for Interpretable Learning of PDEscited by 1
  17. 2026Koopman operator theory: fundamentals, control, and applicationscited by 1
  18. 2023Data driven modeling for self-similar dynamicscited by 0
  19. 2023Featurizing Koopman Mode Decomposition For Robust Forecastingcited by 0
  20. 2024Predicting AI Agent Behavior through Approximation of the Perron-Frobenius Operatorcited by 0
  21. 2025Global Description of Flutter Dynamics via Koopman Theorycited by 0
  22. 2025Physics-Informed Neural Controlled Differential Equations for Scalable Long Horizon Multi-Agent Motion Forecastingcited by 0
  23. 2026RHYME-XT: A Neural Operator for Spatiotemporal Control Systemscited by 0
  24. 2026Dynamic robotic cloth folding with efficient Koopman operator-based model predictive controlcited by 0
  25. 2026Convex Hybrid Modeling: An Operator-Based Approachcited by 0
  26. 2026Dynamic Neural Koopman Distillation for Real-Time Robot Control Using Diffusion Modelscited by 0
  27. 2026Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training errorcited by 0
  28. 2026Learning to control switching nonlinear systems with Koopman operator regressioncited by 0
  29. 2026Data-driven Koopman mode approximation: A neural power iteration algorithmcited by 0
  30. 2026Demystifying Linear Operator Learning for Control Systemscited by 0