相关论文: Incremental Singular Value Decomposition Based Mod…

Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the…

Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…

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…

Dynamic Mode Decomposition (DMD) is a useful tool to effectively extract the dominant dynamic flow structure from a unsteady flow field. However, DMD requires massive computational resources with respect to memory consumption and the usage…

In this work we present a novel methodology that combines Higher Order Singular Value Decomposition (HOSVD) with Deep Learning (DL) techniques for super-resolution in computational fluid dynamics (CFD) and sparse experimental datasets. This…

Singular value decomposition is widely used in modal analysis, such as proper orthogonal decomposition and resolvent analysis, to extract key features from complex problems. SVD derivatives need to be computed efficiently to enable the…

In this paper, we propose hybrid data-driven ROM closures for fluid flows. These new ROM closures combine two fundamentally different strategies: (i) purely data-driven ROM closures, both for the velocity and the pressure; and (ii)…

Resolvent analysis is a powerful tool for studying coherent structures in turbulent flows. However, its application beyond canonical flows with symmetries that can be used to simplify the problem to inherently three-dimensional flows and…

Singular Value Decomposition (SVD) has recently seen a surge of interest as a simple yet powerful tool for large language models (LLMs) compression, with a growing number of works demonstrating 20-80% parameter reductions at minimal…

Reduced order models (ROMs) have achieved a lot of success in reducing the computational cost of traditional numerical methods across many disciplines. For convection-dominated (e.g., turbulent) flows, however, standard ROMs generally yield…

Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…

We present a novel reduced-order fluid simulation technique leveraging Dynamic Mode Decomposition (DMD) to achieve fast, memory-efficient, and user-controllable subspace simulation. We demonstrate that our approach combines the strengths of…

In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we proposed an incremental SVD algorithm with respect to a weighted inner product to compute the proper orthogonal decomposition (POD) of a set of…

Forecasting atmospheric flows with traditional discretization methods, also called full order methods (e.g., finite element methods or finite volume methods), is computationally expensive. We propose to reduce the computational cost with a…

Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade…

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…

Computational physics simulation can be a powerful tool to accelerate industry deployment of new scientific technologies. However, it must address the challenge of computationally tractable, moderately accurate prediction at large industry…

The main goal of this work is to develop a data-driven Reduced Order Model (ROM) strategy from high-fidelity simulation result data of a Full Order Model (FOM). The goal is to predict at lower computational cost the time evolution of…

This article applies low-cost singular value decomposition (lcSVD) for the first time, to the authors knowledge, on combustion reactive flow databases. The lcSVD algorithm is a novel approach to SVD, suitable for calculating high-resolution…

We introduce methodology to construct an emulator for environmental and ecological spatio-temporal processes that uses the higher order singular value decomposition (HOSVD) as an extension of singular value decomposition (SVD) approaches to…