Work

Gaussian Process Koopman Mode Decomposition

Year: 2022

Type: article

Abstract: 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: 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 data set, we show that various analyses are available using the estimated parameters.

Source: Neural Computation

DOI: 10.1162/neco_a_01555

Authors: Takahiro Kawashima, Hideitsu Hino

Institutions: RIKEN Center for Advanced Intelligence Project, The Institute of Statistical Mathematics

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Japan Society for the Promotion of Science, Core Research for Evolutional Science and Technology

Awards: A Study on Methods for Extracting Deterministic Governing Equations from Complex Time Series, G3658334539, G5277313638, G7053381585