mlsanityData to 7 Oct 2026

Leveraging KANs For Enhanced Deep Koopman Operator Discovery

arXiv 2406.02875 ↗First posted 5 Jun 2024cs.LG math.DS physics.app-phcited by 9

Not on the map. Why?

Abstract (arXiv)

Multi-layer perceptrons (MLP's) have been extensively utilized in discovering Deep Koopman operators for linearizing nonlinear dynamics. With the emergence of Kolmogorov-Arnold Networks (KANs) as a more efficient and accurate alternative to the MLP Neural Network, we propose a comparison of the performance of each network type in the context of learning Koopman operators with control. In this work, we propose a KANs-based deep Koopman framework with applications to an orbital Two-Body Problem (2BP) and the pendulum for data-driven discovery of linear system dynamics. KANs were found to be superior in nearly all aspects of training; learning 31 times faster, being 15 times more parameter efficiency, and predicting 1.25 times more accurately as compared to the MLP Deep Neural Networks (DNNs) in the case of the 2BP. Thus, KANs shows potential for being an efficient tool in the development of Deep Koopman Theory.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 12 of its 25 references that are in the map. First posted on arXiv 5 Jun 2024.

Builds on

12 of 25 references.

References · 12

  1. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  2. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  3. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  4. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
  5. 2022ExSpliNet: An interpretable and expressive spline-based neural networkcited by 33
  6. 2019Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Controlcited by 14
  7. 2020Deep Neural Networks with Koopman Operators for Modeling and Control of Autonomous Vehiclescited by 11
  8. 2022Neural Koopman Lyapunov Controlcited by 11
  9. 2021Data-Driven Models for Control Engineering Applications Using the Koopman Operatorcited by 6
  10. 2023Vehicular Applications of Koopman Operator Theory -- A Surveycited by 5
  11. 2023Computationally Efficient Data-Driven Discovery and Linear Representation of Nonlinear Systems For Controlcited by 4
  12. 2024Deep Learning Based Dynamics Identification and Linearization of Orbital Problems using Koopman Theorycited by 3

Built on by

Cited by year

Citing papers per year: 2024: 7; 2025: 2.

9 papers.

  1. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
  2. 2024A Survey on Kolmogorov-Arnold Networkcited by 67
  3. 2024On the expressiveness and spectral bias of KANscited by 36
  4. 2024rKAN: Rational Kolmogorov-Arnold Networkscited by 31
  5. 2024Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networkscited by 11
  6. 2024KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics examplecited by 4
  7. 2024On the relationship between Koopman operator approximations and neural ordinary differential equations for data-driven time-evolution predictionscited by 3
  8. 2025Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometriescited by 3
  9. 2025MLPs and KANs for data-driven learning in physical problems: A performance comparisoncited by 1