Related papers: Gaussian Process Koopman Mode Decomposition
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…
This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on the Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown that the proposed technique…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
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…
In this work, we consider a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models. By exploiting process operation data, both process modeling and state estimation design are…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of…
We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution…
This paper tackles the data-driven approximation of unknown dynamical systems using Koopman-operator methods. Given a dictionary of functions, these methods approximate the projection of the action of the operator on the finite-dimensional…
Common workflows in machine learning and statistics rely on the ability to partition the information in a data set into independent portions. Recent work has shown that this may be possible even when conventional sample splitting is not…
When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Clinical patient records are an example of high-dimensional data that is typically collected from disparate sources and comprises of multiple likelihoods with noisy as well as missing values. In this work, we propose an unsupervised…
We report a new approach to estimating power system inertia directly from time-series data on power system dynamics. The approach is based on the so-called Koopman Mode Decomposition (KMD) of such dynamic data, which is a nonlinear…
We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression which provides a…