Gaussian Process Koopman Mode Decomposition

TL;DR

This paper introduces a probabilistic Gaussian process model for Koopman mode decomposition that estimates eigenvalues, eigenfunctions, modes, and latent variables simultaneously, improving analysis of complex dynamical systems.

Contribution

It presents a novel unsupervised Gaussian process framework for Koopman mode decomposition, enabling joint estimation of key quantities and latent states, with an efficient low-rank covariance approximation strategy.

Findings

Successfully applied to synthetic data and epidemiological dataset.

Provides comprehensive analysis using estimated parameters.

Enhances existing Koopman methods with probabilistic modeling.

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.