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Related papers: Space-time POD-Galerkin approach for parametric fl…

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In this paper, a stabilized proper orthogonal decomposition (POD) reduced-order model (ROM) is presented for the barotropic vorticity equation. We apply the POD-ROM model to mid-latitude simplified oceanic basins, which are standard…

Fluid Dynamics · Physics 2018-01-29 Omer San , Traian Iliescu

We introduce improved Reduced Order Models (ROM) for convection-dominated flows. These non-linear closure models are inspired from successful numerical stabilization techniques used in Large Eddy Simulations (LES), such as Local Projection…

Numerical Analysis · Mathematics 2017-11-28 Mejdi Azaïez , Tomás Chacón Rebollo , Samuele Rubino

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

A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…

Optimization and Control · Mathematics 2019-04-25 Branimir Novoselnik , Vedrana Spudić , Mato Baotić

Model predictive control is a powerful framework for enabling optimal control of constrained systems. However, for systems that are described by high-dimensional state spaces this framework can be too computationally demanding for real-time…

Systems and Control · Electrical Eng. & Systems 2020-08-24 Joseph Lorenzetti , Marco Pavone

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

Numerical Analysis · Mathematics 2025-05-26 Anna Ivagnes , Giovanni Stabile , Gianluigi Rozza

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…

Numerical Analysis · Mathematics 2022-12-21 Niccolò Tonicello , Andrea Lario , Gianluigi Rozza , Gianmarco Mengaldo

These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…

Optimization and Control · Mathematics 2016-09-04 Michael Muehlebach , Raffaello D'Andrea

Chemical reactions modeled by ordinary differential equations are finite-dimensional dissipative dynamical systems with multiple time-scales. They are numerically hard to tackle -- especially when they enter an optimal control problem as…

Optimization and Control · Mathematics 2017-03-27 Marcus Heitel , Dirk Lebiedz

The present work considers the optimal control of a convective Cahn-Hilliard system, where the control enters through the velocity in the transport term. We prove the existence of a solution to the considered optimal control problem. For an…

Optimization and Control · Mathematics 2018-03-08 Carmen Gräßle , Michael Hinze , Nicolas Scharmacher

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

Numerical Analysis · Mathematics 2026-01-05 Ruo Li , Haoyang Liu , Jun Yin

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…

Fluid Dynamics · Physics 2021-12-15 Shady E. Ahmed , Omer San , Adil Rasheed , Traian Iliescu

Stochastic Galerkin methods offer unexplored potential for the numerical simulation of parabolic problems with random variables, in particular if they are combined with variational discretizations of the space and time variables. Due to the…

Numerical Analysis · Mathematics 2026-05-21 Moataz Dawor , Nils Margenberg , Markus Bause

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

Reduced order modeling (ROM) aims to mitigate computational complexity by reducing the size of a high-dimensional state space. In this study, we demonstrate the efficiency, accuracy, and stability of proper orthogonal decomposition…

Atmospheric and Oceanic Physics · Physics 2025-04-17 Yusuf Aydogdu , Navaratnam Sri Namachchivaya

In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical…

Numerical Analysis · Mathematics 2019-11-19 Giovanni Stabile , Bojana Rosic

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

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

Computational Physics · Physics 2021-02-03 Elizabeth H. Krath , Forrest L. Carpenter , Paul G. A. Cizmas , David A. Johnston

In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…

Numerical Analysis · Mathematics 2018-07-04 Lingling Ma , Qiuqi Li , Lijian Jiang

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the…

Numerical Analysis · Mathematics 2023-11-16 Hendrik Fischer , Julian Roth , Ludovic Chamoin , Amelie Fau , Mary F. Wheeler , Thomas Wick