# Leveraging KANs For Enhanced Deep Koopman Operator Discovery

arXiv: https://arxiv.org/abs/2406.02875 · HTML: https://mlsanity.com/paper/2406.02875/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Builds on (most cited first, 12 of 12)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [ExSpliNet: An interpretable and expressive spline-based neural network](https://mlsanity.com/paper/2205.01510/) (2022)
- [Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control](https://mlsanity.com/paper/1911.08751/) (2019)
- [Deep Neural Networks with Koopman Operators for Modeling and Control of Autonomous Vehicles](https://mlsanity.com/paper/2007.02219/) (2020)
- [Neural Koopman Lyapunov Control](https://mlsanity.com/paper/2201.05098/) (2022)
- [Data-Driven Models for Control Engineering Applications Using the Koopman Operator](https://mlsanity.com/paper/2112.07983/) (2021)
- [Vehicular Applications of Koopman Operator Theory -- A Survey](https://mlsanity.com/paper/2303.10471/) (2023)
- [Computationally Efficient Data-Driven Discovery and Linear Representation of Nonlinear Systems For Control](https://mlsanity.com/paper/2309.04074/) (2023)
- [Deep Learning Based Dynamics Identification and Linearization of Orbital Problems using Koopman Theory](https://mlsanity.com/paper/2403.08965/) (2024)

## Built on by (most cited first, 10 of 10)

- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (2024)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.08026/) (2024)
- [KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics example](https://mlsanity.com/paper/2408.02743/) (2024)
- [On the relationship between Koopman operator approximations and neural ordinary differential equations for data-driven time-evolution predictions](https://mlsanity.com/paper/2411.12940/) (2024)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [MLPs and KANs for data-driven learning in physical problems: A performance comparison](https://mlsanity.com/paper/2504.11397/) (2025)
- [Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches](https://mlsanity.com/paper/2604.16842/) (2026)

## 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.