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We develop a structure-preserving parametric model reduction approach for linearized swing equations where parametrization corresponds to variations in operating conditions. We employ a global basis approach to develop the parametric…

Systems and Control · Electrical Eng. & Systems 2021-02-11 Bita Safaee , Serkan Gugercin

Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are…

Dynamical Systems · Mathematics 2025-06-03 Sebastian Resch-Schopper , Romain Rumpler , Gerhard Müller

Reduced basis methods are projection-based model order reduction techniques for reducing the computational complexity of solving parametrized partial differential equation problems. In this work we discuss the design of pyMOR, a freely…

Mathematical Software · Computer Science 2019-10-30 René Milk , Stephan Rave , Felix Schindler

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

We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits…

Numerical Analysis · Mathematics 2023-01-24 Sridhar Chellappa , Lihong Feng , Peter Benner

This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…

Numerical Analysis · Mathematics 2022-04-21 Hannah Lu , Daniel M. Tartakovsky

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…

Numerical Analysis · Mathematics 2025-10-14 Margarita Chasapi , Pablo Antolin , Annalisa Buffa

In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general intercalation battery cell on the basis of non-equilibrium…

Numerical Analysis · Mathematics 2021-10-13 M. Landstorfer , M. Ohlberger , S. Rave , M. Tacke

Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…

Numerical Analysis · Mathematics 2022-03-18 Pierfrancesco Siena , Michele Girfoglio , Gianluigi Rozza

Predictive high-fidelity finite element simulations of human cardiac mechanics co\-mmon\-ly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics.…

Computational Engineering, Finance, and Science · Computer Science 2020-02-18 Martin R. Pfaller , Maria Cruz Varona , Johannes Lang , Cristóbal Bertoglio , Wolfgang A. Wall

This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework…

Numerical Analysis · Mathematics 2025-10-14 Margarita Chasapi , Pablo Antolin , Annalisa Buffa

This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…

Numerical Analysis · Mathematics 2023-08-08 Efthymios N. Karatzas , Francesco Ballarin , Gianluigi Rozza

In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodology is the use of coarse-proxy models (i.e., lower…

Numerical Analysis · Mathematics 2019-11-14 Philip A. Etter , Yuwei Fan , Lexing Ying

In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…

Numerical Analysis · Mathematics 2021-06-07 Kevin Tolle , Nicole Marheineke

We propose a method for the construction of preconditioners of parameter-dependent matrices for the solution of large systems of parameter-dependent equations. The proposed method is an interpolation of the matrix inverse based on a…

Numerical Analysis · Mathematics 2016-10-26 Olivier Zahm , Anthony Nouy

Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which…

Numerical Analysis · Mathematics 2024-04-03 Patrick Buchfink , Silke Glas , Bernard Haasdonk , Benjamin Unger

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

Machine Learning · Computer Science 2026-04-17 Vladimir Fanaskov , Vladislav Trifonov , Alexander Rudikov , Ekaterina Muravleva , Ivan Oseledets

This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…

Numerical Analysis · Mathematics 2022-05-26 Cyril Touzé , Alessandra Vizzaccaro , Olivier Thomas

We present a partitioned Model Order Reduction method for multiphysics problems, that is based on a semi-implicit treatment of the coupling conditions, and on a projection scheme. The proposed Reduced Order Method is based on the Proper…

Numerical Analysis · Mathematics 2023-08-08 Monica Nonino , Francesco Ballarin , Gianluigi Rozza , Yvon Maday

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

Numerical Analysis · Mathematics 2020-08-26 Han Gao , Jian-Xun Wang , Matthew J. Zahr