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Bubble columns are present in several applications, such as chemical and biochemical reactors and petrochemical and environmental engineering industries. This variety of applications is why understanding the bubble columns' dynamics is…
While time-frequency analysis provides rich representations of multicomponent signals, current decomposition methods often overlook the morphological structure where components manifest as distinct regions. This study introduces…
The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with…
We introduce the dynamics mode decomposition for monitoring wide-area power grid networks from sparse measurement data. The mathematical framework fuses data from multiple sensors based on multivariate statistics, providing accurate full…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is…
Modeling wave energy converters (WECs) to accurately predict their hydrodynamic behavior has been a challenge for the wave energy field. Often, this results in either low-fidelity, linear models that break down in energetic seas, or…
Proper orthogonal decomposition (POD) is often employed in developing reduced-order models (ROM) in fluid flows for design, control, and optimization. Contrary to the usual practice where velocity field is the focus, we apply the POD…
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…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
Dynamic Mode Decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of turbulence and is closely related to Koopman…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
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…
Orthogonal Frequency Division Multiplexing (OFDM) is the dominant waveform in modern wireless systems, but suffers performance degradation in high-mobility environments due to Doppler-induced inter-carrier interference and unreliable…
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…
The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures…
We propose a hybrid quantum-classical algorithm for ground state energy (GSE) estimation that remains robust to highly noisy data and exhibits low sensitivity to hyperparameter tuning. Our approach -- Fourier Denoising Observable Dynamic…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…