Related papers: Dynamic Mode Decomposition for data-driven analysi…
The Dynamic Mode Decomposition (DMD)---a popular method for performing data-driven Koopman spectral analysis---has gained increased adoption as a technique for extracting dynamically meaningful spatio-temporal descriptions of fluid flows…
Time domain simulations are crucial for analyzing transient behavior and broadband responses in electromagnetic problems. However, conventional numerical methods such as finite element method in time domain (FEMTD) and finite difference…
In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…
Parametric data-driven reduced-order models (ROMs) that embed dependencies in a large number of input parameters are crucial for enabling many-query tasks in large-scale problems. These tasks, including design optimization, control, and…
Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems…
This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method…
Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. In this work, we develop data-driven reduced-order models (ROMs) for…
A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…
Dynamic Mode Decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of turbulence and is closely related to Koopman…
Time domain simulations of electromagnetic problems are highly valuable in engineering applications, as they allow for the analysis of transient behavior and broadband responses. These simulations utilize time stepping schemes, where each…
We develop an on-the-fly reduced-order model (ROM) integrated with a flow simulation, gradually replacing a corresponding full-order model (FOM) of a physics solver. Unlike offline methods requiring a separate FOM-only simulation prior to…
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…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
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…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a…
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…
This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…
Harmonic instability occurs frequently in the power electronic converter system. This paper leverages multi-resolution dynamic mode decomposition (MR-DMD) as a data-driven diagnostic tool for the system stability of power electronic…
Partial differential equations (PDEs) are widely used for modeling various physical phenomena. These equations often depend on certain parameters, necessitating either the identification of optimal parameters or the solution of the…