mlsanityData to 7 Oct 2026

PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator

arXiv 2306.12962 ↗First posted 22 Jun 2023eess.SY cs.LG cs.SYcited by 10

Not on the map. Why?

Abstract (arXiv)

PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system. The Koopman operator is a principled linear embedding of nonlinear dynamics and facilitates the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. In particular, PyKoopman provides tools for data-driven system identification for unforced and actuated systems that build on the equation-free dynamic mode decomposition (DMD) and its variants. In this work, we provide a brief description of the mathematical underpinnings of the Koopman operator, an overview and demonstration of the features implemented in PyKoopman (with code examples), practical advice for users, and a list of potential extensions to PyKoopman. Software is available at http://github.com/dynamicslab/pykoopman

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 33 of its 88 references that are in the map. First posted on arXiv 22 Jun 2023.

Builds on

33 of 88 references.

References · 33

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  4. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  5. 2017PDE-Net: Learning PDEs from Datacited by 304
  6. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  7. 2017Learning Koopman Invariant Subspaces for Dynamic Mode Decompositioncited by 156
  8. 2018Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networkscited by 155
  9. 2017Linearly-Recurrent Autoencoder Networks for Learning Dynamicscited by 142
  10. 2017VAMPnets: Deep learning of molecular kineticscited by 135
  11. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
  12. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 133
21 more
  1. 2014Dynamic mode decomposition with controlcited by 128
  2. 2019Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systemscited by 96
  3. 2021PySINDy: A comprehensive Python package for robust sparse system identificationcited by 88
  4. 2017Data-driven discovery of Koopman eigenfunctions for controlcited by 64
  5. 2017Time-lagged autoencoders: Deep learning of slow collective variables for molecular kineticscited by 64
  6. 2019Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stabilitycited by 53
  7. 2020From Fourier to Koopman: Spectral Methods for Long-term Time Series Predictioncited by 50
  8. 2016Generalizing Koopman Theory to allow for inputs and controlcited by 49
  9. 2021Deeptime: a Python library for machine learning dynamical models from time series datacited by 36
  10. 2022Residual Dynamic Mode Decomposition: Robust and verified Koopmanismcited by 36
  11. 2018Optimal construction of Koopman eigenfunctions for prediction and controlcited by 34
  12. 2017Koopman operator-based model reduction for switched-system control of PDEscited by 31
  13. 2019Active Learning of Dynamics for Data-Driven Control Using Koopman Operatorscited by 31
  14. 2021Koopman Q-learning: Offline Reinforcement Learning via Symmetries of Dynamicscited by 27
  15. 2022The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systemscited by 21
  16. 2020Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems with Unknown Dynamicscited by 18
  17. 2020Data-Driven Model Predictive Control using Interpolated Koopman Generatorscited by 17
  18. 2020Derivative-Based Koopman Operators for Real-Time Control of Robotic Systemscited by 12
  19. 2020Sparsity-promoting algorithms for the discovery of informative Koopman invariant subspacescited by 10
  20. 2017Parametric Gaussian Process Regression for Big Datacited by 4
  21. 2023Data-Driven Encoding: A New Numerical Method for Computation of the Koopman Operatorcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 4; 2026: 4.

10 papers.

  1. 2024CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilationcited by 7
  2. 2025Universal Learning of Nonlinear Dynamicscited by 5
  3. 2025The Seismic Wavefield Common Task Frameworkcited by 5
  4. 2026CTF4Nuclear: Common Task Framework for Nuclear Fission and Fusion Modelscited by 4
  5. 2024Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximationscited by 3
  6. 2025Information Shapes Koopman Representationcited by 3
  7. 2025kooplearn: A Scikit-Learn Compatible Library of Algorithms for Evolution Operator Learningcited by 1
  8. 2026Scalable Data-Driven Reachability Analysis and Control via Koopman Operators with Conformal Coverage Guaranteescited by 1
  9. 2026LC-SAC: Lyapunov-Constrained Soft Actor-Critic via Koopman Operator Theory for Trajectory Tracking and Stabilizationcited by 1
  10. 2026Physics-informed reduced-order modelling with equivariant spectral submanifoldscited by 0