Parameter Inversion of High-Dimensional Chaotic Systems Using Neural Ordinary Differential Equations

High-dimensional chaotic systems possess complex structural characteristics, which have potential research value in fields like encrypted communication and chaos control. The inverse problem of parameters in high-dimensional chaotic systems is of significant importance for a profound understanding of the dynamic properties of such systems. This article takes a departure from neural ordinary differential equations and embeds the structural dynamics of the dynamical systems to the parameter inversion of high-dimensional chaotic systems. Numerical experiments on different high-dimensional chaotic systems indicate that neural ordinary differential equations perform exceptionally well in solving these inversion problems, with low errors and strong robustness.