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Related papers: H2 Model Order Reduction: A Relative Error Setting

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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

A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order…

Numerical Analysis · Mathematics 2007-05-23 Roland W. Freund

The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…

Machine Learning · Computer Science 2025-05-14 Xinghua Liu , Ming Cao

An approach to derive low-complexity models describing thermal radiation for the sake of simulating the behavior of electric arcs in switchgear systems is presented. The idea is to approximate the (high dimensional) full-order equations,…

Optimization and Control · Mathematics 2015-12-09 Lorenzo Fagiano , Rudolf Gati

The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on…

Dynamical Systems · Mathematics 2020-03-19 Ion Victor Gosea , Mihaly Petreczky , John Leth , Rafael Wisniewski , Athanasios C. Antoulas

We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions…

Systems and Control · Electrical Eng. & Systems 2023-03-01 Mian Muhammad Arsalan Asif , Mian Ilyas Ahmad , Peter Benner , Lihong Feng , Tatjana Stykel

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…

Data Structures and Algorithms · Computer Science 2010-09-28 Petros Drineas , Michael W. Mahoney , S. Muthukrishnan , Tamas Sarlos

In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress…

Numerical Analysis · Mathematics 2014-05-26 Pierre Kerfriden , Juan José Ródenas García , Stéphane Pierre-Alain Bordas

We formulate here an approach to model reduction that is well-suited for linear time-invariant control systems that are stabilizable and detectable but may otherwise be unstable. We introduce a modified $\mathcal{H}_2$-error metric, the…

Numerical Analysis · Mathematics 2019-10-01 Tobias Breiten , Chris A. Beattie , Serkan Gugercin

In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…

Numerical Analysis · Mathematics 2026-04-13 Elise Bonnet-Weill , Virginie Ehrlacher , Luca Nenna

In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…

Systems and Control · Electrical Eng. & Systems 2024-12-20 Maria Cruz Varona , Raphael Gebhart , Julian Suk , Boris Lohmann

We discuss structure-preserving model order reduction for port-Hamiltonian systems based on an approximation of the full-order state by a linear combination of ansatz functions which depend themselves on the state of the reduced-order…

Numerical Analysis · Mathematics 2023-05-16 Philipp Schulze

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…

Numerical Analysis · Mathematics 2019-10-04 Youngsoo Choi , Peter Brown , Bill Arrighi , Robert Anderson

$\mathcal{H}_2$-optimal model order reduction algorithms represent a significant class of techniques, known for their accuracy, which has been extensively validated over the past two decades. Among these, the Iterative Rational Krylov…

Systems and Control · Electrical Eng. & Systems 2024-08-22 Umair Zulfiqar

The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…

Optimization and Control · Mathematics 2007-07-26 Paulo Tabuada , Aaron D. Ames , Agung Julius , George J. Pappas

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

Numerical Analysis · Mathematics 2019-04-15 Roland Pulch

Deep learning models incorporating linear SSMs have gained attention for capturing long-range dependencies in sequential data. However, their large parameter sizes pose challenges for deployment on resource-constrained devices. In this…

Machine Learning · Computer Science 2025-07-31 Hiroki Sakamoto , Kazuhiro Sato

We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…

Dynamical Systems · Mathematics 2017-07-07 Zoran Tomljanović , Christopher Beattie , Serkan Gugercin

This paper presents an H2-optimal model order reduction (MOR) method for linear systems with quadratic outputs based on Riemannian optimization. The H2-optimal MOR is formulated as an optimization problem in which the optimization variables…

Optimization and Control · Mathematics 2026-05-12 Xiaolong Wang , Chenglong Liu

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based…

Optimization and Control · Mathematics 2007-06-14 Bernard Hanzon , Jan M. Maciejowski , Chun Tung Chou