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Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency in solving physical problems. However, the applicability of the method to non linear high-dimensional dynamical systems…

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous…

Numerical Analysis · Mathematics 2022-01-04 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

Numerical Analysis · Mathematics 2020-05-19 Oleg Balabanov , Anthony Nouy

We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier--Stokes equations (NSE). In the proposed approach, the presence of simulated…

Fluid Dynamics · Physics 2022-09-08 Saddam Hijazi , Melina Freitag , Niels Landwehr

This paper introduces a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least-squares Petrov-Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike…

Numerical Analysis · Mathematics 2022-03-24 Payton Lindsay , Jeffrey Fike , Irina Tezaur , Kevin Carlberg

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…

Fluid Dynamics · Physics 2024-05-01 Pierfrancesco Siena , Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

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

This article presents a Galerkin projection-based reduced-order modelling (ROM) approach for segregated fluid-structure interaction (FSI) problems, formulated within an Arbitrary Lagrangian Eulerian (ALE) framework at low Reynolds numbers…

Numerical Analysis · Mathematics 2025-07-24 Valentin Nkana Ngan , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

Dynamical Systems · Mathematics 2026-03-19 Akira Saito , Masato Tanaka

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the…

Numerical Analysis · Mathematics 2023-11-16 Hendrik Fischer , Julian Roth , Ludovic Chamoin , Amelie Fau , Mary F. Wheeler , Thomas Wick

The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian…

Numerical Analysis · Mathematics 2017-03-08 Yuezheng Gong , Qi Wang , Zhu Wang

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

Numerical Analysis · Computer Science 2019-06-07 Kookjin Lee , Kevin Carlberg

A data-driven closure modeling based on proper orthogonal decomposition (POD) temporal modes is used to obtain stable and accurate reduced order models (ROMs) of unsteady compressible flows. Model reduction is obtained via Galerkin and…

Fluid Dynamics · Physics 2021-09-22 Victor Zucatti , William Wolf

POD--Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam…

Numerical Analysis · Mathematics 2017-11-30 Francesco Ballarin , Gianluigi Rozza , Yvon Maday

We propose, analyze, and investigate numerically a novel two-level Galerkin reduced order model (2L-ROM) for the efficient and accurate numerical simulation of the steady Navier-Stokes equations. In the first step of the 2L-ROM, a…

Numerical Analysis · Mathematics 2022-11-24 Dylan Park , Changhong Mou , Honghu Liu , Adrian Sandu , Traian Iliescu

In this paper, we propose an a-priori error estimate for the model order reduction (MOR) method of space-time proper orthogonal decomposition (space-time POD). The original space-time POD approach extends standard POD by reducing not only…

Numerical Analysis · Mathematics 2026-04-27 Carmen Gräßle , Jan Heiland , Jannis Marquardt

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, 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

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…

Numerical Analysis · Mathematics 2019-09-11 Marie Billaud-Friess , Anthony Nouy

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

Numerical Analysis · Mathematics 2023-08-08 Francesco Ballarin , Gianluigi Rozza , Maria Strazzullo