  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.
