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Related papers: Model order reduction via Lie groups

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In this work, we focus on reduced order modeling (ROM) techniques for hyperbolic conservation laws with application in uncertainty quantification (UQ) and in conjunction with the well-known Monte Carlo sampling method. Because we are…

Numerical Analysis · Mathematics 2018-08-13 R. Crisovan , D. Torlo , R. Abgrall , S. Tokareva

In this paper, a parametric model order reduction (pMOR) technique is proposed to find a simplified system representation of a large-scale and complex thermal system. The main principle behind this technique is that any change of the…

Systems and Control · Computer Science 2018-03-15 Daming Lou , Siep Weiland

The objective of this paper is to develop a global non-intrusive Parametric Model Order Reduction (PMOR) methodology for the problem of changing well locations in an oil field, that can eventually be used for well placement optimization to…

Computational Engineering, Finance, and Science · Computer Science 2020-01-16 Hardikkumar Zalavadia , Eduardo Gildin

In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems…

Optimization and Control · Mathematics 2017-12-04 Pawan Goyal , Martin Redmann

In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with…

Numerical Analysis · Mathematics 2023-12-06 Fabian Key , Max von Danwitz , Francesco Ballarin , Gianluigi Rozza

Classical model reduction techniques project the governing equations onto linear subspaces of the high-dimensional state-space. For problems with slowly decaying Kolmogorov-n-widths such as certain transport-dominated problems, however,…

Numerical Analysis · Mathematics 2021-12-22 Patrick Buchfink , Silke Glas , Bernard Haasdonk

The field of model order reduction (MOR) is growing in importance due to its ability to extract the key insights from complex simulations while discarding computationally burdensome and superfluous information. We provide an overview of MOR…

Nuclear Theory · Physics 2022-09-14 J. A. Melendez , C. Drischler , R. J. Furnstahl , A. J. Garcia , Xilin Zhang

In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the…

Robotics · Computer Science 2018-08-07 Paul Chauchat , Axel Barrau , Silvère Bonnabel

We propose a projection-based monolithic model order reduction (MOR) procedure for a class of problems in nonlinear mechanics with internal variables. The work is is motivated by applications to thermo-hydro-mechanical (THM) systems for…

Numerical Analysis · Mathematics 2021-09-14 Angelo Iollo , Giulia Sambataro , Tommaso Taddei

In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear…

Numerical Analysis · Mathematics 2025-01-08 Silke Glas , Benjamin Unger

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

We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…

Numerical Analysis · Mathematics 2025-10-30 Abbas Kabalan , Fabien Casenave , Felipe Bordeu , Virginie Ehrlacher , Alexandre Ern

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

This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as \emph{exact} polynomial optimization problems that can be relaxed as…

Robotics · Computer Science 2023-05-24 Sangli Teng , Ashkan Jasour , Ram Vasudevan , Maani Ghaffari

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…

Numerical Analysis · Mathematics 2019-11-19 Nicola Demo , Marco Tezzele , Gianluigi Rozza

A model-order reduction framework for the meshless smoothed-particle hydrodynamics (SPH) method is presented. The proposed framework introduces the concept of modal reference spaces to overcome the challenges of discovering low-dimensional…

We describe a new method to formulate classical Lagrangian mechanics on a finite-dimensional Lie group. This new approach is much more pedagogical than many previous treatments of the subject, and it directly introduces students to…

Classical Physics · Physics 2011-11-08 A. Lucas

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

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

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