Gaussian Process Koopman Mode Decomposition
This work addresses a specific challenge in dynamical systems analysis for researchers in fields like epidemiology, though it appears incremental as it builds on existing data-driven methods with a probabilistic extension.
The paper tackles the problem of simultaneously estimating Koopman mode decomposition quantities and latent variables in unknown dynamical systems by proposing a nonlinear probabilistic generative model based on an unsupervised Gaussian process, and it demonstrates the model's applicability through analyses on synthetic and real-world epidemiological data.
In this paper, we propose a nonlinear probabilistic generative model of Koopman mode decomposition based on an unsupervised Gaussian process. Existing data-driven methods for Koopman mode decomposition have focused on estimating the quantities specified by Koopman mode decomposition, namely, eigenvalues, eigenfunctions, and modes. Our model enables the simultaneous estimation of these quantities and latent variables governed by an unknown dynamical system. Furthermore, we introduce an efficient strategy to estimate the parameters of our model by low-rank approximations of covariance matrices. Applying the proposed model to both synthetic data and a real-world epidemiological dataset, we show that various analyses are available using the estimated parameters.