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Several nonlinear model reduction techniques are compared for the three cases of the non-parallel version of the Kuramoto-Sivashinsky equation, the transient regime of flow past a cylinder at $Re=100$ and fully developed flow past a…

Computational Physics · Physics 2020-05-08 Denis Sipp , Miguel Fosas de Pando , Peter J. Schmid

Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models…

Fluid Dynamics · Physics 2019-02-25 Jörn Sesterhenn , Amir Shahirpour

This paper deals with the numerical modeling of flow around and through a porous obstacle by a reduced order model (ROM) obtained by Galerkin projection of the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD) reduced…

Fluid Dynamics · Physics 2023-07-24 Cyrille Allery , Claudine Beghein , Claire Dubot , Fabien Dubot

We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…

Numerical Analysis · Mathematics 2021-07-21 Gerhard Kirsten

We aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in…

Numerical Analysis · Mathematics 2022-08-17 Andrea Lario , Romit Maulik , Oliver T. Schmidt , Gianluigi Rozza , Gianmarco Mengaldo

Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning…

Computational Physics · Physics 2023-03-20 Jorio Cocola , John Tencer , Francesco Rizzi , Eric Parish , Patrick Blonigan

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…

Numerical Analysis · Mathematics 2023-11-17 Junming Duan , Jan S. Hesthaven

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

This paper presents the development of a graph autoencoder architecture capable of performing projection-based model-order reduction (PMOR) using a nonlinear manifold least-squares Petrov-Galerkin (LSPG) projection scheme. The architecture…

Computational Engineering, Finance, and Science · Computer Science 2025-09-09 Liam K. Magargal , Parisa Khodabakhshi , Steven N. Rodriguez , Justin W. Jaworski , John G. Michopoulos

This paper presents a new technique for developing reduced-order models (ROMs) for nonlinear radiative transfer problems in high-energy density physics. The proper orthogonal decomposition (POD) of photon intensities is applied to obtain…

Numerical Analysis · Mathematics 2026-03-18 Joseph M. Coale , Dmitriy Y. Anistratov

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…

Numerical Analysis · Mathematics 2022-03-02 Davide Papapicco , Nicola Demo , Michele Girfoglio , Giovanni Stabile , Gianluigi Rozza

In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally…

Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…

Machine Learning · Computer Science 2023-05-17 Paolo Conti , Giorgio Gobat , Stefania Fresca , Andrea Manzoni , Attilio Frangi

In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…

Numerical Analysis · Mathematics 2024-01-22 Maria Strazzullo , Fabio Vicini

This paper focuses on the efficient numerical algorithms of a three-field Biot's consolidation model. The approach begins with the introduction of innovative monolithic and global-in-time iterative decoupled algorithms, which incorporate…

Numerical Analysis · Mathematics 2025-08-07 Huipeng Gu , Francesco Ballarin , Mingchao Cai , Jingzhi Li

Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of…

Machine Learning · Computer Science 2021-08-30 Rachel Cooper , Andrey A. Popov , Adrian Sandu

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

Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective…

Numerical Analysis · Mathematics 2024-06-05 Guglielmo Padula , Michele Girfoglio , Gianluigi Rozza

High-performance computing enables simulation of high-dimensional physical systems, but downstream analyses such as inverse problems and control remain computationally expensive, motivating model order reduction (MOR) to construct efficient…

Fluid Dynamics · Physics 2026-05-28 Tomoki Koike , Prakash Mohan , Marc T. Henry de Frahan , Elizabeth Qian , Julie Bessac

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