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The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce…

The fluid flow around a bluff body is complex and time dependent, which also contains a wide range of time and length scales. The first few eigenmodes of the proper orthogonal decomposition (POD) of such a flow provide significant insight…

Fluid Dynamics · Physics 2021-11-10 Jahrul Alam , Asokan Variyath

In this article, we propose a two-grid based adaptive proper orthogonal decomposition (POD) method to solve the time dependent partial differential equations. Based on the error obtained in the coarse grid, we propose an error indicator for…

Numerical Analysis · Mathematics 2020-07-24 Xiaoying Dai , Xiong Kuang , Jack Xin , Aihui Zhou

In this work, the dual-weighted residual (DWR) method is applied to obtain a certified incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Rduction with Dual-Weighted…

Numerical Analysis · Mathematics 2023-04-04 Hendrik Fischer , Julian Roth , Thomas Wick , Ludovic Chamoin , Amelie Fau

We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive…

Fluid Dynamics · Physics 2020-07-15 Shady E. Ahmed , Omer San , Diana A. Bistrian , Ionel M. Navon

We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…

Optimization and Control · Mathematics 2015-05-21 Tuğba Akman

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

Optimization and Control · Mathematics 2014-07-30 Matthew J. Zahr , Charbel Farhat

We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods to flows in highly-heterogeneous porous media to extract the dominant coherent structures and derive reduced-order models via Galerkin projection.…

Computational Physics · Physics 2015-06-12 Mehdi Ghommem , Victor M. Calo , Yalchin Efendiev

We present a method for combining proper orthogonal decomposition (POD) bases optimized with respect to different norms into a single complete basis. We produce a basis combining decompositions optimized with respect to turbulent kinetic…

Fluid Dynamics · Physics 2023-03-30 Peder J. Olesen , Azur Hodžić , Clara M. Velte

The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures…

Fluid Dynamics · Physics 2016-04-20 Moritz Sieber , Kilian Oberleithner , Christian Oliver Paschereit

We present a formalism for dissipation-optimized decomposition of the strain rate tensor (SRT) of turbulent flow data using Proper Orthogonal Decomposition (POD). The formalism includes a novel inverse spectral SRT operator allowing the…

We propose a regularization for Reduced Order Models (ROMs) of the quasi-geostrophic equations (QGE) to increase accuracy when the Proper Orthogonal Decomposition (POD) modes retained to construct the reduced basis are insufficient to…

Numerical Analysis · Mathematics 2022-12-01 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

In this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD) for the optimal control of the convective…

Numerical Analysis · Mathematics 2020-05-28 Bülent Karasözen , Murat Uzunca , Tuğba Küçükseyhan

The work provides an integrated pipeline for the model order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, Free-Form Deformation is applied for geometry parametrisation, whereas two different…

Numerical Analysis · Mathematics 2018-03-15 F. Salmoiraghi , A. Scardigli , H. Telib , G. Rozza

Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are two complementary singular-value decomposition (SVD) techniques that are widely used to construct reduced-order models (ROMs) in a variety of fields of science…

Numerical Analysis · Mathematics 2020-02-19 Hannah Lu , Daniel M. Tartakovsky

In this paper, we prove uniform error bounds for proper orthogonal decomposition (POD) reduced order modeling (ROM) of Burgers equation, considering difference quotients (DQs), introduced in [26]. In particular, we study the behavior of the…

Numerical Analysis · Mathematics 2023-02-20 Birgul Koc , Tomás Chacón Rebollo , Samuele Rubino

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

Numerical Analysis · Mathematics 2026-04-27 Dawid Kotowski , Mario Ohlberger

We present a novel reduced-order pressure stabilization strategy based on continuous data assimilation(CDA) for two-dimensional incompressible Navier-Stokes equations. A feedback control term is incorporated into pressure-correction…

Numerical Analysis · Mathematics 2023-04-04 Xi Li , Youcai Xu , Minfu Feng

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…

Pattern Formation and Solitons · Physics 2025-08-12 Alessandro Alla , Rudy Geelen , Hannah Lu

Reduced order modeling (ROM) aims to mitigate computational complexity by reducing the size of a high-dimensional state space. In this study, we demonstrate the efficiency, accuracy, and stability of proper orthogonal decomposition…

Atmospheric and Oceanic Physics · Physics 2025-04-17 Yusuf Aydogdu , Navaratnam Sri Namachchivaya
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