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This paper proposes a data-driven algorithm for model order reduction (MOR) of large-scale wind farms and studies the effects that the obtained reduced-order model (ROM) has when this is integrated into the power grid. With respect to…

Systems and Control · Electrical Eng. & Systems 2024-12-16 Zilong Gong , Junyu Mao , Adrià Junyent-Ferré , Giordano Scarciotti

Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…

Optimization and Control · Mathematics 2023-11-29 Sergey Dolgov , Dante Kalise , Luca Saluzzi

We demonstrate that system identification techniques can provide a basis for effective, non-intrusive model order reduction (MOR) for common circuits that are key building blocks in microelectronics. Our approach is motivated by the…

Systems and Control · Electrical Eng. & Systems 2026-02-18 Joshua Hanson , Paul Kuberry , Biliana Paskaleva , Pavel Bochev

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

Machine Learning · Statistics 2016-09-08 P. S. Koutsourelakis , Elias Bilionis

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

Numerical simulations are crucial for comprehending how engineering structures behave under extreme conditions, particularly when dealing with thermo-mechanically coupled issues compounded by damage-induced material softening. However, such…

Analysis of PDEs · Mathematics 2024-07-03 Qinghua Zhang , Stephan Ritzert , Jian Zhang , Jannick Kehls , Stefanie Reese , Tim Brepols

The Model Order Reduction (MOR) technique can provide compact numerical models for fast simulation. Different from the intrusive MOR methods, the non-intrusive MOR does not require access to the Full Order Models (FOMs), especially system…

Machine Learning · Computer Science 2022-04-20 Qinyu Zhuang , Dirk Hartmann , Hans Joachim Bungartz , Juan Manuel Lorenzi

This work proposes a novel structure-preserving model order reduction (MOR) method for linear, time-invariant port-Hamiltonian (pH) systems. Our goal is to construct a reduced order pH system, which can still be interpreted in the physical…

Optimization and Control · Mathematics 2025-10-16 Silke Glas , Mir Mamunuzzaman , Hongliang Mu , Hans Zwart

Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…

Numerical Analysis · Mathematics 2013-06-04 Maziar Raissi , Padmanabhan Seshaiyer

In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying the dominant subspaces based on the reachability Gramian of a system. Once…

Numerical Analysis · Mathematics 2021-02-16 Martin Redmann , Igor Pontes Duff

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators'…

Numerical Analysis · Computer Science 2015-04-16 Martin Drohmann , Kevin Carlberg

Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally,…

Numerical Analysis · Mathematics 2024-05-21 Robin Herkert , Patrick Buchfink , Bernard Haasdonk

This paper investigates a model reduction problem for linear directed network systems, in which the interconnections among the vertices are described by general weakly connected digraphs. First, the definitions of pseudo controllability and…

Optimization and Control · Mathematics 2019-11-12 Xiaodong Cheng , Jacquelien M. A. Scherpen

We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians…

Numerical Analysis · Mathematics 2017-12-07 Ion Victor Gosea , Mihaly Petreczky , Athanasios C. Antoulas , Christophe Fiter

The model reduction problem for semistable infinite-dimensional control systems is studied in this paper. In relation to these systems, we study an object we call the semistability Gramian, which serves as a generalization of the ordinary…

Optimization and Control · Mathematics 2019-03-25 Ingvar Ziemann , Yishao Zhou

Dynamical systems are ubiquitous and are often modeled using a non-linear system of governing equations. Numerical solution procedures for many dynamical systems have existed for several decades, but can be slow due to high-dimensional…

Machine Learning · Computer Science 2021-09-14 Kaushik Balakrishnan , Devesh Upadhyay

Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…

Numerical Analysis · Mathematics 2024-06-11 Lei-Hong Zhang , Ren-Cang Li

We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order…

Numerical Analysis · Mathematics 2022-02-22 Kathrin Smetana , Tommaso Taddei

In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…

Fluid Dynamics · Physics 2015-08-27 Thibault L. B. Flinois , Aimee S. Morgans , Peter J. Schmid

A parametric model order reduction (MOR) approach for simulating the high dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal decomposition (POD) approach to generate small model…

Numerical Analysis · Mathematics 2021-10-05 Andreas Binder , Onkar Jadhav , Volker Mehrmann