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The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the…

Numerical Analysis · Mathematics 2020-05-07 Andrea Bonito , Albert Cohen , Ronald DeVore , Diane Guignard , Peter Jantsch , Guergana Petrova

This paper deals with the joint reduction of the number of dynamic and algebraic states of a nonlinear differential-algebraic equation (NDAE) model of a power network. The dynamic states depict the internal states of generators, loads,…

Systems and Control · Electrical Eng. & Systems 2024-11-15 Muhammad Nadeem , Ahmad F. Taha

The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…

Numerical Analysis · Mathematics 2023-09-14 Victor Zucatti , Matthew J. Zahr

We investigate model order reduction (MOR) strategies for simulating unsteady hemodynamics within cerebrovascular systems, contrasting a physics-based intrusive approach with a data-driven non-intrusive framework. High-fidelity 3D…

Numerical Analysis · Mathematics 2026-03-20 Rahul Halder , Arash Hajisharifi , Kabir Bakhshaei , Gianluigi Rozza

This paper is concerned with the design of a non-intrusive model order reduction (MOR) for the system of parametric time-domain Maxwell equations. A time- and parameter-independent reduced basis (RB) is constructed by using a two-step…

Numerical Analysis · Mathematics 2021-03-24 Ying Zhao , Liang Li , Kun Li

This paper presents a parametric Model Order Reduction (MOR) method for weakly coupled thermo-mechanical Finite Element (FE) models of machine tools and other similar mechatronic systems. This work proposes a reduction method, Krylov Modal…

Numerical Analysis · Mathematics 2020-09-30 Pablo Hernández-Becerro , Daniel Spescha , Konrad Wegener

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…

Optimization and Control · Mathematics 2023-02-07 Boris Kramer , Serkan Gugercin , Jeff Borggaard

Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding…

Computational Engineering, Finance, and Science · Computer Science 2021-03-10 Abel Sancarlos , Victor Champaney , Jean-Louis Duval , Elias Cueto , Francisco Chinesta

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…

Numerical Analysis · Mathematics 2026-05-27 Rudy Geelen , Laura Balzano , Stephen Wright , Karen Willcox

We discuss the recent developments of projection-based model order reduction (MOR) techniques targeting Hamiltonian problems. Hamilton's principle completely characterizes many high-dimensional models in mathematical physics, resulting in…

Numerical Analysis · Mathematics 2021-09-28 J. S. Hesthaven , C. Pagliantini , N. Ripamonti

In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial…

Dynamical Systems · Mathematics 2023-01-24 Pawan Goyal , Igor Pontes Duff , Peter Benner

Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…

Numerical Analysis · Mathematics 2024-09-30 Cecilia Pagliantini , Federico Vismara

This paper aims at characterizing the approximability of bounded sets in the range of nonlinear operators in Banach spaces by finite-dimensional linear varieties. In particular, the class of operators we consider includes the endpoint maps…

Optimization and Control · Mathematics 2024-07-02 Alexander Zuyev , Lihong Feng , Peter Benner

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition,…

Numerical Analysis · Mathematics 2023-04-26 Thomas Simpson , Konstantinos Vlachas , Anthony Garland , Nikolaos Dervilis , Eleni Chatzi

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

In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems…

Optimization and Control · Mathematics 2017-12-04 Pawan Goyal , Martin Redmann

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

For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…

Numerical Analysis · Mathematics 2023-11-16 Alexander V. Mamonov , Maxim A. Olshanskii

This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of…

In this work, we consider wave propagation in materials characterized by nonlinear properties or damage. To accelerate the simulations of the resulting high-dimensional problems, we apply model order reduction methods. Depending on the…

Numerical Analysis · Mathematics 2026-03-24 Saddam Hijazi , Nikiema Fulgence , Hannah Burmester , Natalie Rauter , Carmen Gräßle