TransOKAN: Transformer operator Kolmogorov-Arnold network and its application to UAV dynamics modeling

Abstract

The challenge of increasing the accuracy of mathematical models for different structures and phenomena continues to be relevant in applied sciences and industrial settings. Quadrotor dynamics modeling using a set of nonlinear differential equations is an example of a mathematical model. Existing numerical methods used to solve this problem cannot operate under the conditions of interference. Scientists have been using traditional numerical methods to solve this problem for a long time. Nowadays, this problem may be solved using an alternative method that uses artificial intelligence. In this article, we present TransOKAN, a physics-informed transformer operator Kolmogorov–Arnold network for the finite-horizon modeling of quadrotor dynamics. The task consists of training a controlled phase flow operator that takes the initial state, control sequence, disturbance sequence, and physical parameters and returns a complete state trajectory of a UAV, which includes its position, Euler angles, translational, and angular velocities. The loss function comprises several components, including consistency loss, residuals of the governing equations, phase space distance loss, stability loss, and initial condition constraints. Taylor- and Chebyshev-KAN representations and full and Linformer attention mechanisms are explored in this study. Our model is compared to existing numerical and machine learning methods, physics-informed models, and neural operators.