🤖 AI Summary
Accurately modeling high-dimensional nonlinear coupled systems under data-scarce conditions remains challenging. To address this, this work proposes an enhanced Extended Dynamic Mode Decomposition (EDMD) method that integrates prior knowledge of subsystem control differential equations into the learning of the Koopman operator. By explicitly embedding the governing control equations into the Koopman operator identification process—a first in the literature—the approach significantly improves modeling stability and predictive accuracy in small-sample regimes. Numerical experiments demonstrate that, compared to conventional EDMD, the proposed method achieves superior reconstruction performance and enhanced robustness on coupled oscillator systems.
📝 Abstract
Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic methods based on the Koopman operator have attracted attention as a powerful tool for analyzing and modeling nonlinear dynamical systems. Extended dynamic mode decomposition (EDMD) is one of the most popular methods to approximate the Koopman operator. However, EDMD is a purely data-driven method, and it could be unstable and inaccurate for coupled systems under limited data availability. In this paper, we propose a method to learn the Koopman operator for coupled systems using the differential equations governing each subsystem. We also demonstrate its effectiveness through numerical experiments on coupled oscillator systems.