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Related papers: Solvents based model reduction of linear systems

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Model order reduction (MOR) is crucial for the design process of integrated circuits. Specifically, the vast amount of passive RLCk elements in electromagnetic models extracted from physical layouts exacerbates the extraction time, the…

This work presents a model reduction approach to the inverse problem in the application of subsurface flows. For the Bayesian inverse problem, the forward model needs to be repeatedly computed for a large number of samples to get a…

Numerical Analysis · Mathematics 2016-04-04 Lijian Jiang , Na Ou

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

Fluid-structure interactions are central to many bio-molecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the immersed boundary method (IBM) for biofluid systems, and to…

Numerical Analysis · Mathematics 2021-10-13 Yushuang Luo , Xiantao Li , Wenrui Hao

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

Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless,…

Systems and Control · Electrical Eng. & Systems 2024-10-30 Joseph Lorenzetti , Andrew McClellan , Charbel Farhat , Marco Pavone

Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…

Quantum Physics · Physics 2021-10-06 Lin-Chun Wan , Chao-Hua Yu , Shi-Jie Pan , Su-Juan Qin , Fei Gao , Qiao-Yan Wen

Modelling of physical systems may be a challenging task when it requires solving large sets of numerical equations. This is the case of photovoltaic (PV) systems which contain many PV modules, each module containing several silicon cells.…

Materials Science · Physics 2015-05-21 S. O. Ojo , S. Grivet-Talocia , M. Paggi

A Block Structure Preserving Model Order Reduction approach is proposed for Integral Equations methods based on the Augmented Electric Field Integral Equation. This approach allows for representing the unknown fields with dedicated…

Computational Engineering, Finance, and Science · Computer Science 2025-11-18 Riccardo Torchio , Sebastian Schöps , Francesco Lucchini

Matrix equations are omnipresent in (numerical) linear algebra and systems theory. Especially in model order reduction (MOR) they play a key role in many balancing based reduction methods for linear dynamical systems. When these systems…

Mathematical Software · Computer Science 2020-05-12 Peter Benner , Martin Köhler , Jens Saak

In the study of micro-swimmers, both artificial and biological ones, many-query problems arise naturally. Even with the use of advanced high performance computing (HPC), it is not possible to solve this kind of problems in an acceptable…

Numerical Analysis · Mathematics 2020-08-04 Nicola Giuliani , Martin W. Hess , Antonio DeSimone , Gianluigi Rozza

In this paper, we propose a model reduction technique for linear parameter varying (LPV) systems based on available tools for fixed-structure controller synthesis. We start by transforming a model reduction problem into an equivalent…

Systems and Control · Electrical Eng. & Systems 2024-03-22 Lennart Heeren , Adwait Datar , Antonio Mendez Gonzalez , Herbert Werner

In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse…

Computational Engineering, Finance, and Science · Computer Science 2023-07-06 Philipp Diercks , Karen Veroy , Annika Robens-Radermacher , Jörg F. Unger

Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…

Numerical Analysis · Mathematics 2016-02-05 Pieter Coulier , Hadi Pouransari , Eric Darve

Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…

Optimization and Control · Mathematics 2017-05-30 Thanh Hieu Le

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

A method for data-driven interpolatory model reduction is presented in this extended abstract. This framework enables the computation of the transfer function values at given interpolation points based on time-domain input-output data only,…

Systems and Control · Electrical Eng. & Systems 2020-05-12 Azka Muji Burohman , Bart Besselink , Jacquelien M. A. Scherpen , M. Kanat Camlibel

This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…

Optimization and Control · Mathematics 2024-08-27 Yukuan Hu , Mengyu Li , Xin Liu , Cheng Meng

In this paper, we focus on model reduction of large-scale bilinear systems. The main contributions are threefold. First, we introduce a new framework for interpolatory model reduction of bilinear systems. In contrast to the existing methods…

Numerical Analysis · Mathematics 2016-10-05 Garret Flagg , Serkan Gugercin

We develop here a computationally effective approach for producing high-quality $\mathcal{H}_\infty$-approximations to large scale linear dynamical systems having multiple inputs and multiple outputs (MIMO). We extend an approach for…

Numerical Analysis · Mathematics 2017-09-22 Alessandro Castagnotto , Christopher Beattie , Serkan Gugercin