Learning Koopman operators for coupled systems via information on governing equations of subsystems
For researchers modeling high-dimensional nonlinear coupled systems, this method leverages partial model knowledge to enhance Koopman operator learning, but it is an incremental improvement over existing EDMD.
The paper proposes a method to learn Koopman operators for coupled systems by incorporating known governing equations of subsystems, improving accuracy and stability over purely data-driven EDMD under limited data. Numerical experiments on coupled oscillators show effectiveness.
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.