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In this paper we study the approximation of a distributed optimal control problem for linear para\-bolic PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis…

Optimization and Control · Mathematics 2015-12-08 Alessandro Alla , Carmen Graessle , Michael Hinze

In this paper we consider the numerical approximation of a semilinear reaction-diffusion model problem (PDEs) by means of reduced order methods (ROMs) based on proper orthogonal decomposition (POD). We focus on the time integration of the…

Numerical Analysis · Mathematics 2026-03-05 Bosco García-Archilla , Alicia García-Mascaraque , Julia Novo

In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal…

Dynamical Systems · Mathematics 2016-05-04 Dan Yu , Suman Chakravorty

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 2024-12-30 Tobias Breiten , Shubhaditya Burela , Philipp Schulze

During the past decade, Model Order Reduction (MOR) has become key enabler for the efficient simulation of large circuit models. MOR techniques based on moment-matching are well established due to their simplicity and computational…

The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that…

Numerical Analysis · Mathematics 2017-05-11 Zeger Bontinck , Oliver Lass , Sebastian Schöps , Oliver Rain

This paper presents a methodology that enables projection-based model reduction for black-box high-fidelity models such as commercial CFD codes. The methodology specifically addresses the situation where the high-fidelity model may be a…

Analysis of PDEs · Mathematics 2017-10-18 S. Ashwin Renganathan , Yingjie Liu , Dimitri N. Mavris

We devise and analyze a reduced basis model order reduction (MOR) strategy for an abstract wave problem with vanishing initial conditions and a source term given by the product of a temporal Ricker wavelet and a spatial profile. Such wave…

Numerical Analysis · Mathematics 2026-02-18 Fernando Henriquez , Matthias Schlottbom

In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…

Optimization and Control · Mathematics 2020-12-18 Sebastian Peitz , Sina Ober-Blöbaum , Michael Dellnitz

In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization,…

Numerical Analysis · Mathematics 2023-08-08 Matteo Zancanaro , Francesco Ballarin , Simona Perotto , Gianluigi Rozza

Proper orthogonal decomposition methods for model reduction utilize information about the solution at certain time and parameter points to generate a reduced space basis. In this paper, we compare two proper orthogonal decomposition methods…

Numerical Analysis · Mathematics 2015-01-12 Tanya Kostova , Geoffrey Oxberry , Kyle Chand , William Arrighi

American put options are among the most frequently traded single stock options, and their calibration is computationally challenging since no closed-form expression is available. Due to the higher flexibility in comparison to European…

Numerical Analysis · Mathematics 2016-11-22 Olena Burkovska , Kathrin Glau , Mirco Mahlstedt , Barbara Wohlmuth

We develop and analyze a posteriori error estimators for a proper orthogonal decomposition-discrete empirical interpolation method (Pod-Deim) reduced order model applied to a parametric Poisson equation posed on a parameter-dependent domain…

Numerical Analysis · Mathematics 2026-04-24 Efthymios N. Karatzas

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…

Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…

Numerical Analysis · Mathematics 2018-11-07 Nicola Demo , Marco Tezzele , Gianluca Gustin , Gianpiero Lavini , Gianluigi Rozza

In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…

Numerical Analysis · Mathematics 2021-11-02 Tobias Leibner , Maja Matis , Mario Ohlberger , Stephan Rave

We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…

Numerical Analysis · Mathematics 2022-02-22 Gobat G. , Opreni A. , Fresca S. , Manzoni A. , Frangi A

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

Dimensionality reduction is crucial for controlling nonlinear partial differential equations (PDE) through a "reduce-then-design" strategy, which identifies a reduced-order model and then implements model-based control solutions. However,…

Systems and Control · Electrical Eng. & Systems 2024-03-05 Xiangyuan Zhang , Saviz Mowlavi , Mouhacine Benosman , Tamer Başar

We present a new surrogate modeling technique for efficient approximation of input-output maps governed by parametrized PDEs. The model is hierarchical as it is built on a full order model (FOM), reduced order model (ROM) and…

Numerical Analysis · Mathematics 2022-12-05 B. Haasdonk , H. Kleikamp , M. Ohlberger , F. Schindler , T. Wenzel