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Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…

Numerical Analysis · Mathematics 2021-11-03 Stefania Fresca , Andrea Manzoni

The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…

Computational Engineering, Finance, and Science · Computer Science 2024-08-23 Lisa Scheunemann , Erik Faust

This work investigates projection-based Reduced-Order Models (ROMs) formulated in the frequency domain, employing a space-time basis constructed with Spectral Proper Orthogonal Decomposition to efficiently represent dominant spatio-temporal…

Fluid Dynamics · Physics 2026-01-12 Xiaodong Li , Davide Lasagna

The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…

Numerical Analysis · Mathematics 2023-09-14 Victor Zucatti , Matthew J. Zahr

In this work, Galerkin projection is used to build Reduced Order Models (ROM) for two-dimensional Rayleigh-B\'enard (RB) convection with no-slip walls. We compare an uncoupled projection approach that uses separate orthonormal bases for…

Fluid Dynamics · Physics 2025-04-07 Enrique Flores-Montoya , André V. G. Cavalieri

The paper studies parametric Reduced Order Models (ROMs) for the Kuramoto--Sivashinsky (KS) and generalized Kuramoto--Sivashinsky (gKS) equations. We consider several POD and POD-DEIM projection ROMs with various strategies for parameter…

Numerical Analysis · Mathematics 2025-02-06 Md Rezwan Bin Mizan , Maxim Olshanskii , Ilya Timofeyev

Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…

Numerical Analysis · Mathematics 2022-03-18 Pierfrancesco Siena , Michele Girfoglio , Gianluigi Rozza

In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form.…

Numerical Analysis · Mathematics 2023-07-19 Süleyman Yıldız , Murat Uzunca , Bülent Karasözen

The Allen-Cahn equation is a gradient system, where the free-energy functional decreases monotonically in time. We develop an energy stable reduced order model (ROM) for a gradient system, which inherits the energy decreasing property of…

Numerical Analysis · Mathematics 2019-01-15 Murat Uzunca , Bülent Karasözen

We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…

Numerical Analysis · Mathematics 2023-11-27 Wietse M. Boon , Nicola R. Franco , Alessio Fumagalli , Paolo Zunino

This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a…

Fluid Dynamics · Physics 2015-10-12 Xuping Xie , David Wells , Zhu Wang , Traian Iliescu

This paper investigates the recently introduced data-driven correction reduced order model (DDC-ROM) in the numerical simulation of the quasi-geostrophic equations. The DDC-ROM uses available data to model the correction term that is…

Fluid Dynamics · Physics 2020-06-24 Changhong Mou , Honghu Liu , David R. Wells , Traian Iliescu

We propose a space-time reduced-order model (ROM) for nonlinear dynamical systems, building upon previous work on linear systems. Whereas most ROMs are space-only in that they reduce only the spatial dimension of the state, the proposed…

Numerical Analysis · Mathematics 2025-11-03 Peter Frame , Aaron Towne

In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and…

Numerical Analysis · Mathematics 2026-05-26 Gabriele Codega , Anna Ivagnes , Nicola Demo , Gianluigi Rozza

We propose a non-intrusive Deep Learning-based Reduced Order Model (DL-ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlinearities. In the first phase, a limited number of high fidelity…

Numerical Analysis · Mathematics 2021-11-25 Stefania Fresca , Giorgio Gobat , Patrick Fedeli , Attilio Frangi , Andrea Manzoni

We propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to treat more complex parametrized domains in an efficient and straightforward way. The impact of…

Numerical Analysis · Mathematics 2019-01-11 Efthymios N. Karatzas , Giovanni Stabile , Leo Nouveau , Guglielmo Scovazzi , Gianluigi Rozza

Reduced Order Models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity Computational Fluid Dynamics (CFD) for accelerating the design and optimization processes in engineering applications. Many industrial…

Numerical Analysis · Mathematics 2026-01-15 Shenhui Ruan , Andreas G. Class , Gianluigi Rozza

In this paper we study the approximation of a distributed optimal control problem for linear para\-bolic PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis…

Optimization and Control · Mathematics 2015-12-08 Alessandro Alla , Carmen Graessle , Michael Hinze

A major goal for reduced-order models of unsteady fluid flows is to uncover and exploit latent low-dimensional structure. Proper orthogonal decomposition (POD) provides an energy-optimal linear basis to represent the flow kinematics, but…

Fluid Dynamics · Physics 2022-03-23 Jared L. Callaham , Steven L. Brunton , Jean-Christophe Loiseau

This paper presents a reduced order approach for transient modeling of multiple moving objects in nonlinear crossflows. The Proper Orthogonal Decomposition method and the Galerkin projection are used to construct a reduced version of the…

Fluid Dynamics · Physics 2021-06-07 My Ha Dao