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The accuracy of the reduced-order model (ROM) mainly depends on the selected basis. Therefore, it is essential to compute an appropriate basis with an efficient numerical procedure when applying ROM to nonlinear problems. In this paper, we…

Numerical Analysis · Mathematics 2021-05-05 Jun-Geol Ahn , Hyun-Ik Yang , Jin-Gyun Kim

We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first…

Numerical Analysis · Mathematics 2026-01-13 Valentin Nkana Ngan , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

Numerical Analysis · Mathematics 2021-10-22 Peter Sentz , Kristian Beckwith , Eric C. Cyr , Luke N. Olson , Ravi Patel

This work focuses on steady and unsteady Navier-Stokes equations in a reduced order modeling framework. The methodology proposed is based on a Proper Orthogonal Decomposition within a levelset geometry description and the problems of…

Numerical Analysis · Mathematics 2023-08-08 Efthymios N. Karatzas , Monica Nonino , Francesco Ballarin , Gianluigi Rozza

A multi-fidelity framework is established and demonstrated for prediction of combustion instabilities in rocket engines. The major idea is to adapt appropriate fidelity modeling approaches for different components in a rocket engine to…

Fluid Dynamics · Physics 2019-05-31 Jiayang Xu , Cheng Huang , Karthik Duraisamy

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

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Machine Learning · Computer Science 2026-01-16 Andrew F. Ilersich , Kevin Course , Prasanth B. Nair

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these…

Numerical Analysis · Computer Science 2020-04-22 Philip A. Etter , Kevin T. Carlberg

We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus…

Classical Physics · Physics 2015-06-11 Pierre Kerfriden , Olivier Goury , Timon Rabczuk , Stephane Pierre-Alain Bordas

Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…

Numerical Analysis · Mathematics 2023-08-08 M. Girfoglio , L. Scandurra , F. Ballarin , G. Infantino , F. Nicolò , A. Montalto , G. Rozza , R. Scrofani , M. Comisso , F. Musumeci

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Graphics · Computer Science 2025-10-01 Yutian Tao , Maurizio Chiaramonte , Pablo Fernandez

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…

Machine Learning · Computer Science 2025-09-11 Robert Stephany , Youngsoo Choi

Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…

Numerical Analysis · Mathematics 2022-01-26 Mario Ohlberger , Stephan Rave

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

Numerical Analysis · Mathematics 2023-08-30 Gianluigi Rozza , Martin Hess , Giovanni Stabile , Marco Tezzele , Francesco Ballarin

We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…

Numerical Analysis · Mathematics 2022-06-29 Xianyi Zeng , Giovanni Stabile , Efthymios N. Karatzas , Guglielmo Scovazzi , Gianluigi Rozza

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Machine Learning · Computer Science 2024-06-06 Victor Matray , Faisal Amlani , Frédéric Feyel , David Néron

Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among…

Numerical Analysis · Mathematics 2021-06-28 Matteo Giacomini , Luca Borchini , Ruben Sevilla , Antonio Huerta

A comprehensive approach for real-time computations using a database of parameterized linear reduced-order models (ROMs) is proposed. The method proceeds by sampling offline ROMs for specific values of the parameters and interpolating…

Numerical Analysis · Mathematics 2015-06-24 David Amsallem , Radek Tezaur , Charbel Farhat

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…

Machine Learning · Computer Science 2026-05-19 Robert Stephany , William Michael Anderson , Youngsoo Choi

This thesis presents recent advances in model order reduction methods with the primary aim to construct online-efficient reduced surrogate models for parameterized multiscale phenomena and accelerate large-scale PDE-constrained parameter…

Numerical Analysis · Mathematics 2022-11-18 Tim Keil