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We propose a new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance…

Numerical Analysis · Mathematics 2018-03-06 Philipp Schulze , Julius Reiss , Volker Mehrmann

Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models…

Fluid Dynamics · Physics 2019-02-25 Jörn Sesterhenn , Amir Shahirpour

Deterministic solutions to the Sn transport equation can be computationally expensive to calculate. Reduced Order Models (ROMs) provide an efficient means of approximating the Full Order Model (FOM) solution. We propose a novel approach for…

Numerical Analysis · Mathematics 2025-12-17 Quincy Huhn , Jean Ragusa , Youngsoo Choi

Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…

Numerical Analysis · Mathematics 2023-08-08 Giuseppe Carere , Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza , Rob Stevenson

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

Machine Learning · Statistics 2021-08-23 Patrick Héas , Cédric Herzet

We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…

Numerical Analysis · Mathematics 2017-06-13 A. Paganini , F. Wechsung , P. E. Farrell

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

Optimization and Control · Mathematics 2014-07-30 Matthew J. Zahr , Charbel Farhat

Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…

Optimization and Control · Mathematics 2025-07-23 Andrea Serani , Giorgio Palma , Jeroen Wackers , Domenico Quagliarella , Stefano Gaggero , Matteo Diez

In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced…

Dynamical Systems · Mathematics 2013-12-17 Dan Yu , Suman Chakravorty

In component shape optimization, the component properties are often evaluated by computationally expensive simulations. Such optimization becomes unfeasible when it is focused on a global search requiring thousands of simulations to be…

Computational Engineering, Finance, and Science · Computer Science 2025-12-08 Lucie Kubíčková , Onřej Gebouský , Jan Haidl , Martin Isoz

Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of complex phenomena. In this work, we analyze the…

Fluid Dynamics · Physics 2020-04-15 M. A. Mendez , M. Balabane , J. -M. Buchlin

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 present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameters space reduction. The physical problem considered is the one of the simulation of the…

Numerical Analysis · Mathematics 2018-10-12 Marco Tezzele , Filippo Salmoiraghi , Andrea Mola , Gianluigi Rozza

An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…

Numerical Analysis · Mathematics 2018-06-27 Jorgen S. Dokken , Simon W. Funke , August Johansson , Stephan Schmidt

We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…

Systems and Control · Electrical Eng. & Systems 2026-04-15 Ananda Chakrabarti , Haitham H. Saleh , Indranil Nayak , Balasubramaniam Shanker , Fernando L. Teixeira , Debdipta Goswami

Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and…

Fluid Dynamics · Physics 2014-12-11 Mihailo R. Jovanović , Peter J. Schmid , Joseph W. Nichols

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

Reduced Order Models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity Computational Fluid Dynamics (CFD) for accelerating the design and optimization processes in engineering applications. Many industrial…

Numerical Analysis · Mathematics 2026-01-15 Shenhui Ruan , Andreas G. Class , Gianluigi Rozza

A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…

Systems and Control · Electrical Eng. & Systems 2021-06-01 Andrea Iannelli , Urban Fasel , Roy S. Smith

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

Numerical Analysis · Mathematics 2026-04-27 Dawid Kotowski , Mario Ohlberger