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The interaction of multiple fluids through a heterogeneous pore space leads to complex pore-scale flow dynamics, such as intermittent pathway flow. The non-local nature of these dynamics, and the size of the 4D datasets acquired to capture…
A novel data-driven method of modal analysis for complex flow dynamics, termed as reduced-order variational mode decomposition (RVMD), has been proposed, combining the idea of the separation of variables and a state-of-the-art nonstationary…
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…
High-fidelity large-eddy simulations are suitable to obtain insight into the complex flow dynamics in extended wind farms. In order to better understand these flow dynamics, we use dynamic mode decomposition (DMD) to analyze and reconstruct…
We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator. The algorithms act on data…
Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…
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…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal…
We present an extension of optimal mode decomposition (OMD) for autonomous systems to systems with controls. The extension is developed along the same lines as the extension of dynamic mode decomposition (DMD) to DMD with control (DMDc).…
Recently, distributed algorithms for power system state estimation have attracted significant attention. Along with such advantages as decomposition, parallelization of the original problem and absence of a central computation unit,…
We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolution of observables, Koopman operators transform complex…
This paper proposes a gray-box stability analysis mechanism based on data-driven dynamic mode decomposition (DMD) for commercial grid-tied power electronics converters with limited information on its control parameters and topology. By…
Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of complex phenomena. In this work, we analyze the…
The derivative-free projection method (DFPM) is an efficient algorithm for solving monotone nonlinear equations. As problems grow larger, there is a strong demand for speeding up the convergence of DFPM. This paper considers the application…
We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…
Signal decomposition (SD) approaches aim to decompose non-stationary signals into their constituent amplitude- and frequency-modulated components. This represents an important preprocessing step in many practical signal processing…
The extraction of the model parameters is as important as the development of compact model itself because simulation accuracy is fully determined by the accuracy of the parameters used. This study proposes an efficient model-parameter…
Modal decomposition methods are important for characterizing the low-dimensional dynamics of complex systems, including turbulent flows. Different methods have varying data requirements and produce modes with different properties. Spectral…
We report a new approach to estimating power system inertia directly from time-series data on power system dynamics. The approach is based on the so-called Koopman Mode Decomposition (KMD) of such dynamic data, which is a nonlinear…