Related papers: A tensor-based dynamic mode decomposition based on…

This paper presents a data-driven method for constructing a Koopman linear model based on the Direct Encoding (DE) formula. The prevailing methods, Dynamic Mode Decomposition (DMD) and its extensions are based on least squares estimates…

This paper introduces a fast algorithm for randomized computation of a low-rank Dynamic Mode Decomposition (DMD) of a matrix. Here we consider this matrix to represent the development of a spatial grid through time e.g. data from a static…

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,…

We present a novel acceleration technique for improving the convergence of source iteration for discrete ordinates transport calculations. Our approach uses the idea of the dynamic mode decomposition (DMD) to estimate the slowly decaying…

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 identification of reduced-order models from high-dimensional data is a challenging task, and even more so if the identified system should not only be suitable for a certain data set, but generally approximate the input-output behavior…

Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time diagonal of such a…

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,…

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…

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…

We introduce a new adaptive decomposition tool, which we refer to as Nonlinear Mode Decomposition (NMD). It decomposes a given signal into a set of physically meaningful oscillations for any waveform, simultaneously removing the noise. NMD…

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…

Homogeneous polynomial dynamical systems (HPDSs), which can be equivalently represented by tensors, are essential for modeling higher-order networked systems, including ecological networks, chemical reactions, and multi-agent robotic…

Magic State Distillation (MSD) has been a research focus for fault-tolerant quantum computing due to the need for non-Clifford resource in gaining quantum advantage. Although many of the MSD protocols so far are based on stabilizer codes…

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).…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

Subsequence clustering of time series is an essential task in data mining, and interpreting the resulting clusters is also crucial since we generally do not have prior knowledge of the data. Thus, given a large collection of tensor time…

This work proposes convolutional-sparse-coded dynamic mode decomposition (CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) and convolutional sparse coding. EDMD is a data driven analysis method for describing a nonlinear…

Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…

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…