Leveraging KANs For Enhanced Deep Koopman Operator Discovery
This work addresses the efficiency and accuracy of deep Koopman operator discovery for nonlinear dynamics, which is incremental as it applies an existing network type (KANs) to a known problem.
The paper tackled the problem of discovering Deep Koopman operators for linearizing nonlinear dynamics by comparing Kolmogorov-Arnold Networks (KANs) to multi-layer perceptrons (MLPs), finding that KANs learned 31 times faster, were 15 times more parameter efficient, and predicted 1.25 times more accurately in the Two-Body Problem.
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.