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A novel reduced-order model (ROM) formulation for incompressible flows is presented with the key property that it exhibits non-linearly stability, independent of the mesh (of the full order model), the time step, the viscosity, and the…

Numerical Analysis · Mathematics 2020-08-12 B. Sanderse

In this paper, a type of novel projection-based, time-segmented reduced order model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems based upon the arbitrary Lagrangian--Eulerian (ALE)-finite element method (FEM) in…

Computational Engineering, Finance, and Science · Computer Science 2024-02-16 Qijia Zhai , Shiquan Zhang , Pengtao Sun , Xiaoping Xie

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

Spatiotemporally chaotic systems, such as the solutions of some nonlinear partial differential equations, are dynamical systems that evolve toward a lower dimensional manifold. This manifold has an intricate geometry with heterogeneous…

Computational Physics · Physics 2025-06-17 Antonio Colanera , Luca Magri

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

A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space-time ROM for linear dynamical problems has been developed, which further reduces the…

Numerical Analysis · Mathematics 2025-11-06 Youngkyu Kim , Karen May Wang , Youngsoo Choi

Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of…

Numerical Analysis · Mathematics 2023-02-17 Ludovica Cicci , Stefania Fresca , Mengwu Guo , Andrea Manzoni , Paolo Zunino

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box.…

Computational Physics · Physics 2024-10-16 Aviral Prakash , Yongjie Jessica Zhang

In this paper, we propose a nonintrusive filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier-Stokes equations in convection-dominated regimes. We propose a novel…

Numerical Analysis · Mathematics 2018-10-23 M. Gunzburger , T. Iliescu , M. Mohebujjaman , M. Schneier

In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical…

Numerical Analysis · Mathematics 2019-11-19 Giovanni Stabile , Bojana Rosic

We introduce a novel nonlinear imaging method for the acoustic wave equation based on data-driven model order reduction. The objective is to image the discontinuities of the acoustic velocity, a coefficient of the scalar wave equation from…

Numerical Analysis · Mathematics 2018-06-18 Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky

We introduce improved Reduced Order Models (ROM) for convection-dominated flows. These non-linear closure models are inspired from successful numerical stabilization techniques used in Large Eddy Simulations (LES), such as Local Projection…

Numerical Analysis · Mathematics 2017-11-28 Mejdi Azaïez , Tomás Chacón Rebollo , Samuele Rubino

We generate data-driven reduced order models (ROMs) for inversion of the one and two dimensional Schr\"odinger equation in the spectral domain given boundary data at a few frequencies. The ROM is the Galerkin projection of the Schr\"odinger…

Numerical Analysis · Mathematics 2020-06-24 Liliana Borcea , Vladimir Druskin , Alexander V. Mamonov , Shari Moskow , Mikhail Zaslavsky

New reduced-order models (ROMs) are derived for sinusoidal shear flow (also known as Waleffe flow) and plane Couette flow in small periodic domains. A first derivation for Waleffe flow exploits Fourier modes that form a natural orthonormal…

Fluid Dynamics · Physics 2021-04-07 André V. G. Cavalieri

Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral methods). Thus,…

Fluid Dynamics · Physics 2020-12-03 Changhong Mou , Zhu Wang , David R. Wells , Xuping Xie , Traian Iliescu

The purpose of this work is to present a reduced order modeling framework for parametrized turbulent flows with moderately high Reynolds numbers within the variational multiscale (VMS) method. The Reduced Order Models (ROMs) presented in…

Numerical Analysis · Mathematics 2023-08-08 Giovanni Stabile , Francesco Ballarin , Giacomo Zuccarino , Gianluigi Rozza

This research paper investigates the Adjoint Petrov-Galerkin (APG) method for reduced order models (ROM) and fluid dynamics governed by the incompressible Navier-Stokes equations. The Adjoint Petrov-Galerkin ROM, derived using the…

Systems and Control · Electrical Eng. & Systems 2026-01-13 Kamil David Sommer , Lucas Mieg , Siddharth Sharma , Romuald Skoda , Martin Mönnigmann

In this paper we develop a numerical method for solving an inverse scattering problem of estimating the scattering potential in a Schr\"{o}dinger equation from frequency domain measurements based on reduced order models (ROM). The ROM is a…

Numerical Analysis · Mathematics 2025-11-10 Andreas Tataris , Tristan van Leeuwen , Alexander V. Mamonov

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…

Computational Engineering, Finance, and Science · Computer Science 2024-09-02 Azzeddine Tiba , Thibault Dairay , Florian de Vuyst , Iraj Mortazavi , Juan-Pedro Berro Ramirez

This paper deals with the development of a Reduced-Order Model (ROM) to investigate haemodynamics in cardiovascular applications. It employs the use of Proper Orthogonal Decomposition (POD) for the computation of the basis functions and the…

Numerical Analysis · Mathematics 2025-01-24 Pierfrancesco Siena , Pasquale Claudio Africa , Michele Girfoglio , Gianluigi Rozza