相关论文: Uncertainty Quantification of Autoencoder-based Ko…

The Koopman operator presents an attractive approach to achieve global linearization of nonlinear systems, making it a valuable method for simplifying the understanding of complex dynamics. While data-driven methodologies have exhibited…

The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman equation, are ubiquitous in reinforcement learning and control theory. However, these equations become intractable for high-dimensional or nonlinear systems. This…

Conserved quantities, i.e. constants of motion, are critical for characterizing many dynamical systems in science and engineering. These quantities are related to underlying symmetries and they provide fundamental knowledge about physical…

One of the fundamental tasks in quantum information theory is quantum data compression, which can be realized via quantum autoencoders that first compress quantum states to low-dimensional ones and then recover to the original ones with a…

A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…

Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…

The Koopman operator framework holds promise for spectral analysis of nonlinear dynamical systems based on linear operators. Eigenvalues and eigenfunctions of the Koopman operator, so-called Koopman eigenvalues and Koopman eigenfunctions,…

The mathematical models used to represent physical phenomena are generally known to be imperfect representations of reality. Model inadequacies arise for numerous reasons, such as incomplete knowledge of the phenomena or computational…

This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…

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…

A learning method is proposed for Koopman operator-based models with the goal of improving closed-loop control behavior. A neural network-based approach is used to discover a space of observables in which nonlinear dynamics is linearly…

In this paper we are concerned with the error-covariance lower-bounding problem in Kalman filtering: a sensor releases a set of measurements to the data fusion/estimation center, which has a perfect knowledge of the dynamic model, to allow…

Koopman operator theory has gained significant attention in recent years for identifying discrete-time nonlinear systems by embedding them into an infinite-dimensional linear vector space. However, providing stability guarantees while…

Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of…

A Transformer-based Koopman autoencoder is proposed for linearizing Fisher's reaction-diffusion equation. The primary focus of this study is on using deep learning techniques to find complex spatiotemporal patterns in the reaction-diffusion…

For the class of continuous, measure-preserving automorphisms on compact metric spaces, a procedure is proposed for constructing a sequence of finite-dimensional approximations to the associated Koopman operator on a Hilbert space. These…

We study the position estimation of a mechanical oscillator undergoing both detuned parametric amplification and continuous quantum measurement. This model, which can be utilised to produce squeezed states, is applied to a general…

This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the…

This paper develops a parametric Koopman operator framework for Stochastic Model Predictive Control (SMPC), where the Koopman operator is parametrized by Polynomial Chaos Expansions (PCEs). The model is learned from data using the Extended…

Global information about dynamical systems can be extracted by analysing associated infinite-dimensional transfer operators, such as Perron-Frobenius and Koopman operators as well as their infinitesimal generators. In practice, these…