mlsanityData to 7 Oct 2026

Online Estimation of the Koopman Operator Using Fourier Features

arXiv 2212.01503 ↗First posted 3 Dec 2022cs.RO cs.LGcited by 4

Not on the map. Why?

Abstract (arXiv)

Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables, acting on states of the dynamical system. This is ad hoc and requires the full dataset for evaluation. In this paper, we offer an optimization scheme to allow joint learning of the observables and Koopman operator with online data. Our results show we are able to reconstruct the evolution and represent the global features of complex dynamical systems.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 14 of its 35 references that are in the map. First posted on arXiv 3 Dec 2022.

Builds on

14 of 35 references.

References · 14

  1. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 125
  2. 2017Data-driven discovery of Koopman eigenfunctions for controlcited by 64
  3. 2016Generalizing Koopman Theory to allow for inputs and controlcited by 49
  4. 2017Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spacescited by 48
  5. 2017Non-Stationary Spectral Kernelscited by 38
  6. 2018Optimal construction of Koopman eigenfunctions for prediction and controlcited by 34
  7. 2019Active Learning of Dynamics for Data-Driven Control Using Koopman Operatorscited by 31
  8. 2019Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Controlcited by 22
  9. 2015Generalized Spectral Kernelscited by 17
  10. 2019Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Controlcited by 14
  11. 2020Episodic Koopman Learning of Nonlinear Robot Dynamics with Application to Fast Multirotor Landingcited by 3
  12. 2021A Convex Optimization Approach to Learning Koopman Operatorscited by 3
2 more
  1. 2021ACD-EDMD: Analytical Construction for Dictionaries of Lifting Functions in Koopman Operator-based Nonlinear Robotic Systemscited by 3
  2. 2021Learning and Leveraging Features in Flow-Like Environments to Improve Situational Awarenesscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 1; 2026: 1.

4 papers.

  1. 2024Koopman-informed recurrent neural networkscited by 8
  2. 2024Spectrally Informed Learning of Fluid Flowscited by 1
  3. 2025KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planningcited by 1
  4. 2026Dictionary learning for Kernel EDMDcited by 0