相关论文: Dynamic Mode Decomposition for Construction of Red…

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…

Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant…

The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…

The present focus of heart flow studies is largely based on flow within the left ventricle and how this flow changes when subject to disease. However, despite recent advancements, a simple tractable model of even healthy left ventricular…

Any deterministic autonomous dynamical system may be globally linearized by its' Koopman operator. This object is typically infinite-dimensional and can be approximated by the so-called Dynamic Mode Decomposition (DMD). In DMD, the central…

Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of…

Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been…

This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order…

We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the…

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…

In this paper, we discuss reduced order modelling approaches to bifurcating systems arising from continuum mechanics benchmarks. The investigation of the beam's deflection is a relevant topic of investigation with fundamental implications…

A data-driven closure modeling based on proper orthogonal decomposition (POD) temporal modes is used to obtain stable and accurate reduced order models (ROMs) of unsteady compressible flows. Model reduction is obtained via Galerkin and…

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…

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…

We present a reduced order method (ROM) based on proper orthogonal decomposition (POD) for the viscous Burgers' equation and the incompressible Navier-Stokes equations discretized using an implicit-explicit hybrid discontinuous…

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential,…

In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts…

Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced…

Flexible spacecraft structures present significant challenges for physical and control system design due to nonlinear dynamics, mission constraints, environmental variables, and changing operational conditions. This paper presents a…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…