English
Related papers

Related papers: A projection-based reduced-order model for paramet…

200 papers

We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…

Numerical Analysis · Mathematics 2021-04-01 Matteo Salvador , Luca Dede' , Andrea Manzoni

In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the…

Numerical Analysis · Mathematics 2023-11-21 Nicola Demo , Marco Tezzele , Gianluigi Rozza

Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…

Numerical Analysis · Mathematics 2017-09-28 Max Gunzburger , Nan Jiang , Michael Schneier

This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of…

In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems.…

Numerical Analysis · Mathematics 2023-08-08 Luca Venturi , Francesco Ballarin , Gianluigi Rozza

Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…

Machine Learning · Statistics 2025-09-16 Xiao Liu , Jingyi Feng , Xinchao Liu

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

Non-intrusive model reduction is a promising solution to system dynamics prediction, especially in cases where data are collected from experimental campaigns or proprietary software simulations. In this work, we present a method for…

Fluid Dynamics · Physics 2024-04-04 Leonidas Gkimisis , Thomas Richter , Peter Benner

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…

Numerical Analysis · Mathematics 2017-06-27 Christoph Lehrenfeld , Arnold Reusken

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical…

Numerical Analysis · Mathematics 2023-11-09 Ivan Prusak , Monica Nonino , Davide Torlo , Francesco Ballarin , Gianluigi Rozza

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

Numerical Analysis · Mathematics 2020-07-02 Thomas Simpson , Nikolaos Dervilis , Eleni Chatzi

In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal…

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

In this paper, we propose an efficient proper orthogonal decomposition based reduced-order model(POD-ROM) for nonstationary Stokes equations, which combines the classical projection method with POD technique. This new scheme mainly owns two…

Numerical Analysis · Mathematics 2023-04-04 Xi Li , Yan Luo , Minfu Feng

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 effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…

Computational Physics · Physics 2018-12-05 Xuping Xie , Guannan Zhang , Clayton G. Webster

We present an online-adaptive hyperreduced reduced basis element method for model order reduction of parameterized, component-based nonlinear systems. The method, in the offline phase, prepares a library of hyperreduced archetype components…

Numerical Analysis · Mathematics 2025-08-27 Mehran Ebrahimi , Masayuki Yano

We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain…

Numerical Analysis · Mathematics 2023-11-01 Tommaso Taddei , Xuejun Xu , Lei Zhang

A non-intrusive reduced order model based on convolutional autoencoders (NIROM-CAEs) is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatio-temporal large-scale physical problems. The…

Fluid Dynamics · Physics 2022-08-08 Azzedine Abdedou , Azzeddine Soulaïmani

In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress…

Numerical Analysis · Mathematics 2014-05-26 Pierre Kerfriden , Juan José Ródenas García , Stéphane Pierre-Alain Bordas

We consider model order reduction based on proper orthogonal decomposition (POD) for unsteady incompressible Navier-Stokes problems, assuming that the snapshots are given by spatially adapted finite element solutions. We propose two…

Numerical Analysis · Mathematics 2019-08-02 Carmen Gräßle , Michael Hinze , Jens Lang , Sebastian Ullmann
‹ Prev 1 3 4 5 6 7 10 Next ›