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We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order…

Numerical Analysis · Mathematics 2022-02-22 Kathrin Smetana , Tommaso Taddei

The main focus of the present work is the inclusion of spatial adaptivity for the snapshot computation in the offline phase of model order reduction utilizing Proper Orthogonal Decomposition (POD-MOR) for nonlinear parabolic evolution…

Numerical Analysis · Mathematics 2020-08-04 Carmen Gräßle , Michael Hinze

In this chapter we introduce a combined parameter and model reduction methodology and present its application to the efficient numerical estimation of a pressure drop in a set of deformed carotids. The aim is to simulate a wide range of…

Numerical Analysis · Mathematics 2023-08-30 Marco Tezzele , Francesco Ballarin , Gianluigi Rozza

The purpose of this work is to introduce a novel POD-Galerkin strategy for the hybrid finite volume/finite element solver introduced in Berm\'udez et al. 2014 and Busto et al. 2018. The interest is into the incompressible Navier-Stokes…

Numerical Analysis · Mathematics 2018-10-19 Saray Busto , Giovanni Stabile , Gianluigi Rozza , María Elena Vázquez-Cendón

POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…

Numerical Analysis · Mathematics 2023-05-09 Simone Brivio , Stefania Fresca , Nicola Rares Franco , Andrea Manzoni

A model-order reduction framework for the meshless smoothed-particle hydrodynamics (SPH) method is presented. The proposed framework introduces the concept of modal reference spaces to overcome the challenges of discovering low-dimensional…

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

Classical Proper Orthogonal Decomposition (POD)-based Galerkin projection models of chaotic flows typically require a large number of modes as well as stabilization or closure terms to achieve adequate accuracy and long-term stability. We…

Computational Physics · Physics 2026-05-27 Anant Kumar , Oliver Morales , Rohit Deshmukh

Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional…

Numerical Analysis · Mathematics 2022-12-06 Toby Phillips , Claire E. Heaney , Paul N. Smith , Christopher C. Pain

The recently developed generalized Fourier-Galerkin method is complemented by a numerical continuation with respect to the kinetic energy, which extends the framework to the investigation of modal interactions resulting in folds of the…

Numerical Analysis · Mathematics 2021-01-07 Malte Krack , Lars Panning-von Scheidt , Jörg Wallaschek

Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation…

Systems and Control · Computer Science 2017-03-21 Xin Du , Peter Benner

This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our…

Fluid Dynamics · Physics 2019-06-26 Omer San , Romit Maulik , Mansoor Ahmed

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Optimization and Control · Mathematics 2026-03-31 Tobias Breiten , Shubhaditya Burela , Philipp Schulze

Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can…

Fluid Dynamics · Physics 2021-02-23 Carlos J. G. Rojas , Andreas Dengel , Mateus Dias Ribeiro

This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method…

Computational Physics · Physics 2020-07-14 Renee Swischuk , Boris Kramer , Cheng Huang , Karen Willcox

This work considers a weighted POD-greedy method to estimate statistical outputs parabolic PDE problems with parametrized random data. The key idea of weighted reduced basis methods is to weight the parameter-dependent error estimate…

Numerical Analysis · Mathematics 2017-12-21 Christopher Spannring , Sebastian Ullmann , Jens Lang

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet number. In this situation, computational instabilities occur, both for steady and…

Numerical Analysis · Mathematics 2024-05-03 Fabio Zoccolan , Maria Strazzullo , Gianluigi Rozza

This work establishes a novel, unified theoretical framework for a class of high order embedded boundary methods, revealing that the Reconstruction for Off-site Data (ROD) treatment shares a fundamental structure with the recently developed…

Numerical Analysis · Mathematics 2026-01-01 Mirco Ciallella

Mathematical modeling often yields linear dynamical systems in science and engineering. We change physical parameters of the system into random variables to perform an uncertainty quantification. The stochastic Galerkin method yields a…

Numerical Analysis · Mathematics 2019-09-17 Roland Pulch

We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…

Numerical Analysis · Mathematics 2026-02-26 Vladimír Lukeš , Eduard Rohan