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In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…

Projection-based nonlinear model order reduction methods can be used to reduce simulation times for the solution of many PDE-constrained problems. It has been observed in literature that such nonlinear reduced-order models (ROMs) based on…

Numerical Analysis · Computer Science 2018-07-02 C. Bach , L. Song , T. Erhart , F. Duddeck

Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…

Fluid Dynamics · Physics 2023-09-22 M. Oulghelou , A. Ammar , R. Ayoub

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

In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation-based domain decomposition approach, we derive an optimal…

Numerical Analysis · Mathematics 2024-02-21 Ivan Prusak , Davide Torlo , Monica Nonino , Gianluigi Rozza

A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of…

Numerical Analysis · Mathematics 2019-12-02 Sokratia Georgaka , Giovanni Stabile , Kelbij Star , Gianluigi Rozza , Michael J Bluck

The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations…

We apply the Postprocessing Galerkin method to a recently introduced continuous data assimilation (downscaling) algorithm for obtaining a numerical approximation of the solution of the two-dimensional Navier-Stokes equations corresponding…

Numerical Analysis · Mathematics 2016-12-22 Cecilia F. Mondaini , Edriss S. Titi

We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse…

Machine Learning · Computer Science 2026-02-27 Ismaël Zighed , Andrea Nóvoa , Luca Magri , Taraneh Sayadi

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

In this paper we consider fully discrete approximations with inf-sup stable mixed finite element methods in space to approximate the Navier-Stokes equations. A continuous downscaling data assimilation algorithm is analyzed in which…

Numerical Analysis · Mathematics 2019-04-15 Bosco García-Archilla , Julia Novo

This paper presents a reduced order approach for transient modeling of multiple moving objects in nonlinear crossflows. The Proper Orthogonal Decomposition method and the Galerkin projection are used to construct a reduced version of the…

Fluid Dynamics · Physics 2021-06-07 My Ha Dao

For incompressible flow models, the pressure term serves as a Lagrange multiplier to ensure that the incompressibility constraint is satisfied. In engineering applications, the pressure term is necessary for calculating important quantities…

Numerical Analysis · Mathematics 2019-09-16 Kiera Kean , Michael Schneier

Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov-)Galerkin projection process that enforces the dynamics to evolve in a low-dimensional subspace of the original…

Computational Engineering, Finance, and Science · Computer Science 2021-04-02 A. Schein , K. T. Carlberg , M. J. Zahr

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

An energy preserving reduced order model is developed for two dimensional nonlinear Schr\"odinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE is discretized in space by the symmetric interior penalty…

Numerical Analysis · Mathematics 2019-01-15 Bülent Karasözen , Murat Uzunca

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce…

Two comprehensive approaches are considered for constructing projection-based reduced-order computational models for linear dynamical systems. The first one reduces the governing equations written in the descriptor form, using a Galerkin or…

Dynamical Systems · Mathematics 2013-01-08 David Amsallem , Charbel Farhat

In recent years, the Adaptive Antoulas-Anderson AAA algorithm has established itself as the method of choice for solving rational approximation problems. Data-driven Model Order Reduction (MOR) of large-scale Linear Time-Invariant (LTI)…

Numerical Analysis · Mathematics 2024-01-19 Tommaso Bradde , Stefano Grivet-Talocia , Quirin Aumann , Ion Victor Gosea

Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such…