Leveraging KANs For Enhanced Deep Koopman Operator Discovery

TL;DR

This paper demonstrates that Kolmogorov-Arnold Networks (KANs) outperform traditional MLPs in learning Deep Koopman operators, offering faster training, better parameter efficiency, and higher accuracy in modeling nonlinear dynamical systems.

Contribution

The paper introduces a KANs-based deep Koopman framework and compares its performance to MLPs, showing significant improvements in efficiency and accuracy for system identification.

Findings

KANs learn Koopman operators 31 times faster than MLPs.

KANs are 15 times more parameter-efficient than MLPs.

KANs achieve 1.25 times higher accuracy in predictions.

Abstract

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.