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Related papers: Energy-based model order reduction for linear stoc…

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In a recent work [Manucci, Unger, ArXiv e-print 2404.10511, 2024], the authors propose using two generalized Lyapunov equations (GLEs) to derive a balancing-based model order reduction~(MOR) method for a general class of switched…

Numerical Analysis · Mathematics 2024-07-30 Mattia Manucci , Benjamin Unger

We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient…

Numerical Analysis · Mathematics 2021-04-14 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

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

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…

Numerical Analysis · Mathematics 2022-12-21 Niccolò Tonicello , Andrea Lario , Gianluigi Rozza , Gianmarco Mengaldo

In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for inviscid fluids in computational fluid dynamics are the Euler…

Numerical Analysis · Mathematics 2024-12-11 Dominic Breit , Thamsanqa Castern Moyo , Philipp Öffner

This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations (PDEs). The vast majority of energy-preserving…

Machine Learning · Computer Science 2024-09-17 Süleyman Yıldız , Pawan Goyal , Peter Benner

An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…

Methodology · Statistics 2026-05-11 Yutong Zhang , Xiao Liu

We devise and analyze a reduced basis model order reduction (MOR) strategy for an abstract wave problem with vanishing initial conditions and a source term given by the product of a temporal Ricker wavelet and a spatial profile. Such wave…

Numerical Analysis · Mathematics 2026-02-18 Fernando Henriquez , Matthias Schlottbom

Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…

Dynamical Systems · Mathematics 2025-02-11 Linus Balicki , Serkan Gugercin

This article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs). We work in Hilbert spaces endowed with a natural inner product including a point…

Chaotic Dynamics · Physics 2015-09-11 Mickaël D. Chekroun , Michael Ghil , Honghu Liu , Shouhong Wang

Density-based topology optimization has become a powerful method for automatically generating optimized designs in a wide variety of applications. However, it comes with a large computational cost when solving the physical model requires…

Numerical Analysis · Mathematics 2026-04-22 Luis Fernando Cusicanqui Lopez , Ramadan Krasniqi , Florian Feppon , Karl Meerbergen

We present a new optimization-based structure-preserving model order reduction (MOR) method for port-Hamiltonian descriptor systems (pH-DAEs) with differentiation index two. Our method is based on a novel parameterization that allows us to…

Systems and Control · Electrical Eng. & Systems 2022-06-09 Tim Moser , Paul Schwerdtner , Volker Mehrmann , Matthias Voigt

We investigate linear dynamical systems consisting of ordinary differential equations with high dimensionality. Model order reduction yields alternative systems of much lower dimensions. However, a reduced system may be unstable, although…

Numerical Analysis · Mathematics 2018-08-14 Roland Pulch

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

Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…

Systems and Control · Computer Science 2018-09-14 T. W. Stegink , C. De Persis , A. J. van der Schaft

This paper presents a parametric Model Order Reduction (MOR) method for weakly coupled thermo-mechanical Finite Element (FE) models of machine tools and other similar mechatronic systems. This work proposes a reduction method, Krylov Modal…

Numerical Analysis · Mathematics 2020-09-30 Pablo Hernández-Becerro , Daniel Spescha , Konrad Wegener

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

Numerical Analysis · Mathematics 2020-05-19 Oleg Balabanov , Anthony Nouy

This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the…

Computational Finance · Quantitative Finance 2021-06-15 Andreas Binder , Onkar Jadhav , Volker Mehrmann

This paper presents a novel model order reduction technique tailored for power systems with a large share of inverter-based energy resources. Such systems exhibit an increased level of dynamic stiffness compared to traditional power…

Systems and Control · Electrical Eng. & Systems 2024-07-08 Simon Muntwiler , Ognjen Stanojev , Andrea Zanelli , Gabriela Hug , Melanie N. Zeilinger

We consider a nonlinear variational wave equation that models the dynamics of the director field in nematic liquid crystals with high molecular rotational inertia. Being derived from an energy principle, energy stability is an intrinsic…

Numerical Analysis · Mathematics 2016-03-31 U. Koley , P. Aursand