Related papers: Data-Driven Koopman Analysis of Tropical Climate S…
We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…
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…
Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative…
Koopman mode decomposition (KMD) is a technique of nonlinear time-series analysis capable of decomposing data on complex spatio temporal dynamics into multiple modes oscillating with single frequencies, called the Koopman modes (KMs). We…
Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network…
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…
With the accumulation of meteorological big data, data-driven models for short-term precipitation forecasting have shown increasing promise. We focus on Koopman operator analysis, which is a data-driven scheme to discover governing laws in…
Real-world time series are characterized by intrinsic non-stationarity that poses a principal challenge for deep forecasting models. While previous models suffer from complicated series variations induced by changing temporal distribution,…
Koopman theory asserts that a nonlinear dynamical system can be mapped to a linear system, where the Koopman operator advances observations of the state forward in time. However, the observable functions that map states to observations are…
The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a…
Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary…
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…
The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data. Building on the recent development of the Koopman model…
A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyse nonlinear dynamical systems brings new strategies for…
Koopman Mode Decomposition (KMD) is a technique of nonlinear time-series analysis that originates from point spectrum of the Koopman operator defined for an underlying nonlinear dynamical system. We present a numerical algorithm of KMD…
Species subject to predation and environmental threats commonly exhibit variable periods of population boom and bust over long timescales. Understanding and predicting such behavior, especially given the inherent heterogeneity and…
Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has…
This paper introduces a data-driven time embedding method for modeling long-range seasonal dependencies in spatiotemporal forecasting tasks. The proposed approach employs Dynamic Mode Decomposition (DMD) to extract temporal modes directly…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
We introduce a method for decomposition of trend, cycle and seasonal components in spatio-temporal models and apply it to investigate the existence of climate changes in temperature and rainfall series. The method incorporates critical…