Related papers: Extreme-Point Symmetric Mode Decomposition Method …
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
The Ensemble Empirical Mode Decomposition (EEMD) has become a preferred technique to decompose nonlinear and non-stationary signals due to its ability to create time-varying basis functions. However, current EEMD signal cleaning techniques…
The Dynamic Mode Decomposition (DMD) and the more general Extended DMD (EDMD) are powerful tools for computational analysis of dynamical systems in data-driven scenarios. They are built on the theoretical foundation of the Koopman…
Time-frequency representation (TFR) allowing for mode reconstruction plays a significant role in interpreting and analyzing the nonstationary signal constituted of various modes. However, it is difficult for most previous methods to handle…
The numerical approximation of solutions of parametric or stochastic hyperbolic PDEs is still a serious challenge. Because of shock singularities, most methods from the elliptic and parabolic regime, such as reduced basis methods, POD or…
We introduce the optimized dynamic mode decomposition algorithm for constructing an adaptive and computationally efficient reduced order model and forecasting tool for global atmospheric chemistry dynamics. By exploiting a low-dimensional…
Current progress in electro-optical modulation within silicon integrated photonics, driven by the unique capabilities of advanced functional materials, has led to significant improvements in device performance. However, inherent constraints…
In this paper, a meshless Hermite-HDMR finite difference method is proposed to solve high-dimensional Dirichlet problems. The approach is based on the local Hermite-HDMR expansion with an additional smoothing technique. First, we introduce…
In this work we consider the problem of semi-active damping optimization of mechanical systems with fixed damper positions. Our goal is to compute a damping that is locally optimal with respect to the $\mathcal{H}_\infty$-norm of the…
We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net…
Civil structures are on the verge of changing which leads energy dissipation capacity to decline. Structural Health Monitoring (SHM) as a process in order to implement a damage detection strategy and assess the condition of structure plays…
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the action of the Koopman operator on a linear function space spanned by a dictionary of functions. The accuracy of EDMD model critically depends on…
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…
Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…
We propose a novel change-point detection method based on online Dynamic Mode Decomposition with control (ODMDwC). Leveraging ODMDwC's ability to find and track linear approximation of a non-linear system while incorporating control…
This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions,…
In this paper, a generic extension of variational mode decomposition (VMD) algorithm for multivariate or multichannel data sets is presented. We first define a model for multivariate modulated oscillations that is based on the presence of a…
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 dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…
Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…