Gaussian Process Koopman Mode Decomposition

Abstract

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.

arXiv comment32 pages, 4 figures, to appear in Neural Computation

References in corpus (4)

• A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
• Sparsity-promoting dynamic mode decomposition
• Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
• Application of Gaussian Process Regression to Koopman Mode Decomposition for Noisy Dynamic Data