  Kolmogorov-Arnold networks (KANs) as an alternative to multi-layer
perceptrons (MLPs) are a recent development demonstrating strong potential for
data-driven modeling. This work applies KANs as the backbone of a neural
ordinary differential equation (ODE) framework, generalizing their use to the
time-dependent and temporal grid-sensitive cases often seen in dynamical
systems and scientific machine learning applications. The proposed KAN-ODEs
retain the flexible dynamical system modeling framework of Neural ODEs while
leveraging the many benefits of KANs compared to MLPs, including higher
accuracy and faster neural scaling, stronger interpretability and
generalizability, and lower parameter counts. First, we quantitatively
demonstrated these improvements in a comprehensive study of the classical
Lotka-Volterra predator-prey model. We then showcased the KAN-ODE framework's
ability to learn symbolic source terms and complete solution profiles in
higher-complexity and data-lean scenarios including wave propagation and shock
formation, the complex Schr\"odinger equation, and the Allen-Cahn phase
separation equation. The successful training of KAN-ODEs, and their improved
performance compared to traditional Neural ODEs, implies significant potential
in leveraging this novel network architecture in myriad scientific machine
learning applications for discovering hidden physics and predicting dynamic
evolution.
