Related papers: The Multiverse of Dynamic Mode Decomposition Algor…

Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…

The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…

The Koopman representation is an infinite dimensional linear representation of linear or nonlinear dynamical systems. It represents the dynamics of output maps (aka observables), which are functions on the state space whose evaluation is…

A new dynamic mode decomposition (DMD) method is introduced for simultaneous online system identification and denoising in conjunction with the adoption of an extended Kalman filter algorithm\color{black}. The present paper explains the…

We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods to flows in highly-heterogeneous porous media to extract the dominant coherent structures and derive reduced-order models via Galerkin projection.…

Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven…

Diffusion models (DMs) have emerged as a powerful class of generative AI models, showing remarkable potential in anomaly detection (AD) tasks across various domains, such as cybersecurity, fraud detection, healthcare, and manufacturing. The…

Aero-optical beam control relies on the development of low-latency forecasting techniques to quickly predict wavefronts aberrated by the Turbulent Boundary Layer (TBL) around an airborne optical system, and its study applies to a…

In Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions. However, manually selecting observable functions that span the invariant subspace of…

Simulating dynamics of open quantum systems is sometimes a significant challenge, despite the availability of various exact or approximate methods. Particularly when dealing with complex systems, the huge computational cost will largely…

In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to…

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…

Presented is an algorithm based on dynamic mode decomposition (DMD) for acceleration of the power method (PM). The power method is a simple technique for determining the dominant eigenmode of an operator $\mathbf{A}$, and variants of the…

This paper presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It is known that DMD and other standard data-driven methods face a fundamental difficulty…

Structural damage detection using non-contact sensing remains a challenging problem in structural health monitoring. This study presents a data-driven framework based on Dynamic Mode Decomposition (DMD) for extracting structural dynamics…

We revisit the setting and the assumptions that underlie the methodology of Dynamic Mode Decomposition (DMD) in order to highlight caveats as well as potential measures of when the applicability is warranted.

Human interpretation of the world encompasses the use of symbols to categorize sensory inputs and compose them in a hierarchical manner. One of the long-term objectives of Computer Vision and Artificial Intelligence is to endow machines…

The strong performance of simple neural networks is often attributed to their nonlinear activations. However, a linear view of neural networks makes understanding and controlling networks much more approachable. We draw from a dynamical…

Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are two complementary singular-value decomposition (SVD) techniques that are widely used to construct reduced-order models (ROMs) in a variety of fields of science…

We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…