Related papers: Scale-Separated Dynamic Mode Decomposition and Ion…
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…
Dynamic Mode Decomposition (DMD) is a numerical method that seeks to fit timeseries data to a linear dynamical system. In doing so, DMD decomposes dynamic data into spatially coherent modes that evolve in time according to exponential…
We propose fully data-driven variational methods, termed successive jump and mode decomposition (SJMD) and its multivariate extension, successive multivariate jump and mode decomposition (SMJMD), for successively decomposing nonstationary…
Time-series forecasting often faces challenges due to data volatility, which can lead to inaccurate predictions. Variational Mode Decomposition (VMD) has emerged as a promising technique to mitigate volatility by decomposing data into…
Streaming Dynamic Mode Decomposition (sDMD) (Hemati et al., Phys. Fluids 26(2014)) is a low-storage version of Dynamic Mode Decomposition (DMD) (Schmid, J. Fluid Mech. 656 (2010)), a data-driven method to extract spatio-temporal flow…
This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It…
Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory…
Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of delay-coordinates embedding and DMD, i.e., delay-coordinates…
The frequency estimation from the Koopman eigenvalues (phase angles) obtained via Dynamic Mode Decomposition (DMD) is addressed. Since the calculations of the frequencies from the phase angles are nonunique, the modifications of DMD for…
This article presents the data-driven equation-free modeling of the dynamics of a hexafloat floating offshore wind turbine based on the application of dynamic mode decomposition (DMD). All the analyses are performed on experimental data…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
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…
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…
This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional…
We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing…
The Dynamic Mode Decomposition (DMD) is a Koopman-based algorithm that straightforwardly isolates individual mechanisms from the compound morphology of direct measurement. However, many may be perplexed by the messages the DMD structures…
A method for measuring the spectrum of a density field by a discrete wavelet space-scale decomposition (SSD) has been studied. We show how the power spectrum can effectively be described by the father function coefficients (FFC) of the…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
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…
Modern computational science and engineering applications are being improved by the advances in scientific machine learning. Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal…