Related papers: Deep Koopman Learning using Noisy Data

Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…

We consider the problem of designing almost optimal predictors for dynamical systems from a finite sequence of noisy observations and incomplete knowledge of the dynamics and the noise. We first discuss the properties of the optimal (Bayes)…

In this paper, a novel Koopman-type inverse operator for linear time-invariant non-minimum phase systems with stochastic disturbances is proposed. This operator employs functions of the desired output to directly calculate the input.…

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…

This paper introduces a reduced order modeling technique based on Koopman operator theory that gives confidence bounds on the model's predictions. It is based on a data-driven spectral decomposition of the Koopman operator. The reduced…

In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant…

Koopman operator theory provides a global linear representation of nonlinear dynamics and underpins many data-driven methods. In practice, however, finite-dimensional feature spaces induced by a user-chosen dictionary are rarely invariant,…

The Koopman operator approach for data-driven control design of a nonlinear system is on the rise because of its capability to capture the behaviours of global dynamics. However, the measurement noises of inputs and outputs will bias the…

Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD) and its generalization, the extended-DMD (EDMD), are…

Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of…

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 long-timescale behavior of complex dynamical systems can be described by linear Markov or Koopman models in a suitable latent space. Recent variational approaches allow the latent space representation and the linear dynamical model to…

kooplearn is a machine-learning library that implements linear, kernel, and deep-learning estimators of dynamical operators and their spectral decompositions. kooplearn can model both discrete-time evolution operators (Koopman/Transfer) and…

Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the…

This paper explores the problem of training a recurrent neural network from noisy data. While neural network based dynamic predictors perform well with noise-free training data, prediction with noisy inputs during training phase poses a…

The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…

The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…

Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is a necessary step to draw conclusions from these data, and it often becomes quite essential to construct dynamical models using these…

This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…

This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics…