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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

In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…

Numerical Analysis · Mathematics 2018-08-29 Lijie Ji , Yanlai Chen , Zhenli Xu

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

Numerical Analysis · Mathematics 2020-05-19 Oleg Balabanov , Anthony Nouy

In this article we investigate model order reduction of large-scale systems using time-limited balanced truncation, which restricts the well known balanced truncation framework to prescribed finite time intervals. The main emphasis is on…

Numerical Analysis · Mathematics 2018-01-08 Patrick Kürschner

A model order reduction algorithm is presented that generates a reduced-order model of the original high-order model, which ensures high-fidelity within the desired time interval. The reduced model satisfies a subset of the first-order…

Systems and Control · Electrical Eng. & Systems 2020-07-16 Umair Zulfiqar , Victor Sreeram , Xin Du

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

Parametric high-fidelity simulations are of interest for a wide range of applications. But the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order…

Numerical Analysis · Mathematics 2019-02-28 Patrick Buchfink , Ashish Bhatt , Bernard Haasdonk

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

Fluid Dynamics · Physics 2020-04-13 Ali Thari , Vito Pasquariello , Niels Aage , Stefan Hickel

In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model order reduction is to construct local reduced spaces that…

Numerical Analysis · Mathematics 2019-10-29 Andreas Buhr , Laura Iapichino , Mario Ohlberger , Stephan Rave , Felix Schindler , Kathrin Smetana

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…

Fluid Dynamics · Physics 2018-02-23 Andrew J. Majda , Di Qi

An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…

Systems and Control · Electrical Eng. & Systems 2024-08-13 Umair Zulfiqar , Zhi-Hua Xiao , Qiu-Yan Song , Mohammad Monir Uddin , Victor Sreeram

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…

Optimization and Control · Mathematics 2021-08-25 Kainat Khowaja , Mykhaylo Shcherbatyy , Wolfgang Karl Härdle

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

Numerical Analysis · Mathematics 2021-10-22 Peter Sentz , Kristian Beckwith , Eric C. Cyr , Luke N. Olson , Ravi Patel

In [Z. Hu, R. Li, and Z. Qiao. Acceleration for microflow simulations of high-order moment models by using lower-order model correction. J. Comput. Phys., 327:225-244, 2016], it has been successfully demonstrated that using lower-order…

Numerical Analysis · Mathematics 2019-05-14 Zhicheng Hu , Guanghui Hu

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Machine Learning · Computer Science 2026-01-16 Andrew F. Ilersich , Kevin Course , Prasanth B. Nair

We present a data-driven nonintrusive model order reduction method for dynamical systems with moving boundaries. The proposed method draws on the proper orthogonal decomposition, Gaussian process regression, and moving least squares…

Computational Engineering, Finance, and Science · Computer Science 2021-03-18 Zhan Ma , Wenxiao Pan

This paper presents a novel model order reduction technique tailored for power systems with a large share of inverter-based energy resources. Such systems exhibit an increased level of dynamic stiffness compared to traditional power…

Systems and Control · Electrical Eng. & Systems 2024-07-08 Simon Muntwiler , Ognjen Stanojev , Andrea Zanelli , Gabriela Hug , Melanie N. Zeilinger

Partial differential equation-based numerical solution frameworks for initial and boundary value problems have attained a high degree of complexity. Applied to a wide range of physics with the ultimate goal of enabling engineering…

Numerical Analysis · Mathematics 2021-05-11 Matthew Duschenes , Krishna Garikipati

A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…

Numerical Analysis · Mathematics 2025-12-01 Philippe-André Luneau , Jean Deteix

The paper proposes an approach for the efficient model order reduction of dynamic contact problems in linear elasticity. Instead of the augmented Lagrangian method that is widely used for mechanical contact problems, we prefer here the…

Numerical Analysis · Mathematics 2021-07-27 Diana Manvelyan , Bernd Simeon , Utz Wever