Related papers: Data-driven spectral analysis of the Koopman opera…
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…
We introduce a linear operator on a Hilbert $C^*$-module for analyzing skew-product dynamical systems. The operator is defined by composition and multiplication. We show that it admits a decomposition in the Hilbert $C^*$-module, called…
Koopman operator provides a general linear description of nonlinear systems, whose estimation from data (via extended dynamic mode decomposition) has been extensively studied. However, the elusiveness between the Koopman spectrum and the…
For a compact complex manifold endowed with a big line bundle and a Radon measure, we study the localization phenomena of the associated Bergman (or Christoffel-Darboux) kernel. For Bernstein-Markov measures, this results in the…
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…
This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…
In this paper, a data-driven nonparametric approach is presented for forecasting the probability density evolution of stochastic dynamical systems. The method is based on stochastic Koopman operator and extended dynamic mode decomposition…
This paper presents a data-driven method for constructing a Koopman linear model based on the Direct Encoding (DE) formula. The prevailing methods, Dynamic Mode Decomposition (DMD) and its extensions are based on least squares estimates…
We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator theory. Given a system in which some components of the state…
Any deterministic autonomous dynamical system may be globally linearized by its' Koopman operator. This object is typically infinite-dimensional and can be approximated by the so-called Dynamic Mode Decomposition (DMD). In DMD, the central…
With the advancement of sensing and communication in power networks, high-frequency real-time data from a power network can be used as a resource to develop better monitoring capabilities. In this work, a systematic approach based on…
This work establishes a rigorous bridge between infinite-dimensional delay dynamics and finite-dimensional Koopman learning, with explicit and interpretable error guarantees. While Koopman analysis is well-developed for ordinary…
Koopman operator theory provides a powerful data-driven technique for modeling nonlinear dynamical systems in a linear framework, in comparison to computationally expensive and highly nonlinear physics-based simulations. However, Koopman…
Mean field control provides a robust framework for coordinating large-scale populations with complex interactions and has wide applications across diverse fields. However, the inherent nonlinearity and the presence of unknown system…
This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…
We develop a Koopman operator framework for studying the {computational properties} of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ``Koopman…
The Dynamic Mode Decomposition (DMD)---a popular method for performing data-driven Koopman spectral analysis---has gained increased adoption as a technique for extracting dynamically meaningful spatio-temporal descriptions of fluid flows…
We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a…
Complex systems, such as pathophysiological processes, commonly exhibit chaotic, nonlinear, and intermittent phenomena. Koopman operator theory and Hankel alternative view of Koopman (HAVOK) model have been widely used to decompose the…