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Related papers: Model order reduction via Lie groups

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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

We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie…

Numerical Analysis · Mathematics 2025-11-18 L. Blanco , F. Jiménez Alburquerque , J. de Lucas , C. Sardón

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

Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM)…

Machine Learning · Computer Science 2026-03-04 Hrishikesh Viswanath , Yue Chang , Aleksey Panas , Julius Berner , Peter Yichen Chen , Aniket Bera

In this paper we discuss a projection model order reduction (MOR) method for a class of parametric linear evolution PDEs, which is based on the application of the Laplace transform. The main advantage of this approach consists in the fact…

Numerical Analysis · Mathematics 2022-09-02 Nicola Guglielmi , Mattia Manucci

We present an adaptive sampling strategy for the optimization-based structure preserving model order reduction (MOR) algorithm developed in [Schwerdtner, P. and Voigt, M. (2020). Structure preserving model order reduction by parameter…

Systems and Control · Electrical Eng. & Systems 2021-06-23 Paul Schwerdtner , Matthias Voigt

In the aim of reducing the computational cost of the resolution of parameter-dependent eigenvalue problems, a model order reduction (MOR) procedure is proposed. We focus on the case of non-self-adjoint generalized eigenvalue problems, such…

Numerical Analysis · Mathematics 2023-11-27 Yonah Conjungo Taumhas , Geneviève Dusson , Virginie Ehrlacher , Tony Lelièvre , François Madiot

Dynamical systems are pervasive in almost all engineering and scientific applications. Simulating such systems is computationally very intensive. Hence, Model Order Reduction (MOR) is used to reduce them to a lower dimension. Most of the…

Numerical Analysis · Mathematics 2020-03-31 Navneet Pratap Singh , Kapil Ahuja

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

Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents a data-driven approach using reduced order models (ROM) to efficiently model non-equilibrium flows…

Fluid Dynamics · Physics 2023-10-09 Julian Koellermeier , Philipp Krah , Julius Reiss , Zachary Schellin

Adaptive tracking control for rigid body dynamics is of critical importance in control and robotics, particularly for addressing uncertainties or variations in system model parameters. However, most existing adaptive control methods are…

Robotics · Computer Science 2025-02-11 Jiawei Tang , Shilei Li , Ling Shi

Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized (stochastic) partial differential equations and hence reduce computational complexity. A particular class of MOR techniques is balancing…

Optimization and Control · Mathematics 2019-03-29 Martin Redmann

Model order reduction (MOR) techniques play a crucial role in the computer-aided design of modern integrated circuits, where they are used to reduce the size of parasitic networks. Unfortunately, the efficient reduction of passive networks…

Computational Engineering, Finance, and Science · Computer Science 2016-06-29 Denis Oyaro , Piero Triverio

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

Dynamical Systems · Mathematics 2026-05-14 Dan Wilson

We investigate the time domain model order reduction (MOR) framework using general orthogonal polynomials by Jiang and Chen 2012 and extend their idea by exploiting the structure of the corresponding linear system of equations. Identifying…

Numerical Analysis · Mathematics 2021-05-10 Manuela Hund , Jens Saak

We extend the Euler Poincare formalism from Lie groups to Lie groupoids for optimal control problems. While Lie algebroids provide the standard infinitesimal framework, the groupoid formulation enables global trajectory reconstruction and…

Dynamical Systems · Mathematics 2026-05-26 Ghorbanali Haghighatdoost

For an easy use of model order reduction techniques in applications, software solutions are needed. In this paper, we describe the MORLAB, Model Order Reduction LABoratory, toolbox as an efficient implementation of model reduction…

Mathematical Software · Computer Science 2021-09-07 Peter Benner , Steffen W. R. Werner

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…

Machine Learning · Computer Science 2021-06-18 Zhe Bai , Liqian Peng

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the…

Numerical Analysis · Mathematics 2023-11-16 Hendrik Fischer , Julian Roth , Ludovic Chamoin , Amelie Fau , Mary F. Wheeler , Thomas Wick

Model Order Reduction (MOR) methods enable the generation of real-time-capable digital twins, which can enable various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems,…

Numerical Analysis · Mathematics 2021-09-09 Qinyu Zhuang , Juan Manuel Lorenzi , Hans-Joachim Bungartz , Dirk Hartmann