Gaussian Process Koopman Mode Decomposition.

Area of Science:

• Dynamical Systems and Control Theory
• Machine Learning
• Statistical Modeling

Background:

• Data-driven Koopman mode decomposition methods typically focus on estimating eigenvalues, eigenfunctions, and modes.
• Existing techniques often struggle with simultaneous estimation of these quantities and latent variables.

Purpose of the Study:

• To propose a nonlinear probabilistic generative model for Koopman mode decomposition using unsupervised Gaussian processes.
• To enable simultaneous estimation of Koopman quantities and latent variables governed by an unknown dynamical system.

Main Methods:

• Development of an unsupervised Gaussian process-based nonlinear probabilistic generative model.
• Implementation of an efficient parameter estimation strategy using low-rank approximations of covariance matrices.

Main Results:

• The proposed model successfully estimates Koopman eigenvalues, eigenfunctions, modes, and latent variables simultaneously.
• Validation on both synthetic and real-world epidemiological datasets demonstrates the model's efficacy.

Conclusions:

• The novel Gaussian process model offers a powerful tool for analyzing dynamical systems.
• The method facilitates diverse analyses through estimated parameters, advancing Koopman mode decomposition applications.