Related papers: Residual Dynamic Mode Decomposition: Robust and ve…
Nonlinear phenomena can be analyzed via linear techniques using operator-theoretic approaches. Data-driven method called the extended dynamic mode decomposition (EDMD) and its variants, which approximate the Koopman operator associated with…
In this two-part article, we evaluate the utility and the generalizability of the Dynamic Mode Decomposition (DMD) algorithm for data-driven analysis and reduced-order modelling of plasma dynamics in cross-field ExB configurations. The DMD…
Dynamic mode decomposition (DMD) is a versatile approach that enables the construction of low-order models from data. Controller design tasks based on such models require estimates and guarantees on predictive accuracy. In this work, we…
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…
Data-driven dimensionality reduction methods such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have proven to be useful for exploring complex phenomena within fluid dynamics and beyond. A well-known…
Analyzing the spectral properties of the Koopman operator is crucial for understanding and predicting the behavior of complex stochastic dynamical systems. However, the accuracy of data-driven estimation methods, such as Extended Dynamic…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a…
We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix…
The correlation and extraction of coherent structures from a turbulent flow is a principle objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into…
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…
Reduced-order models (ROMs) are very popular for surrogate modeling of full-order computational fluid dynamics (CFD) simulations, allowing for real-time approximation of complex flow phenomena. However, their application to CFD models…
The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…
Within this work, we investigate how data-driven numerical approximation methods of the Koopman operator can be used in practical control engineering applications. We refer to the method Extended Dynamic Mode Decomposition (EDMD), which…
Dynamic Mode Decomposition (DMD) and its extensions (EDMD) have been at the forefront of data-based approaches to Koopman operators. Most (E)DMD algorithms assume that the entire state is sampled at a uniform sampling rate. In this paper,…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant…
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the Koopman operator for deterministic and stochastic (control) systems. This operator is linear and encompasses full information on the (expected…
Dynamic mode decomposition (DMD) and its variants have emerged as popular methods for the post-processing of fluid dynamics' simulations in order to visualize dominant coherent structures and to reduce the practical degrees of freedom to a…
Dynamic Mode Decomposition (DMD) has received increasing research attention due to its capability to analyze and model complex dynamical systems. However, it faces challenges in computational efficiency, noise sensitivity, and difficulty…