English
Related papers

Related papers: On the stability of projection-based linear reduce…

200 papers

We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based…

Computational Engineering, Finance, and Science · Computer Science 2024-05-15 Clément Vella , Pierre Gosselet , Serge Prudhomme

In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to…

Systems and Control · Electrical Eng. & Systems 2024-04-02 Xuewen Zhang , Minghao Han , Xunyuan Yin

We provide two solutions to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only. Both of our solutions are global, employ the…

Optimization and Control · Mathematics 2011-08-24 Iasson Karafyllis , Miroslav Krstic

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 adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…

Computational Physics · Physics 2023-08-09 Cheng Huang , Karthik Duraisamy

We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a…

Numerical Analysis · Mathematics 2020-06-11 Federico Pichi , Annalisa Quaini , Gianluigi Rozza

Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…

Machine Learning · Computer Science 2023-05-17 Paolo Conti , Giorgio Gobat , Stefania Fresca , Andrea Manzoni , Attilio Frangi

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

This work presents a nonintrusive physics-preserving method to learn reduced-order models (ROMs) of Lagrangian systems, which includes nonlinear wave equations. Existing intrusive projection-based model reduction approaches construct…

Numerical Analysis · Mathematics 2024-04-05 Harsh Sharma , Boris Kramer

Projection methods provide an appealing way to construct reduced-order models of large-scale linear dynamical systems: they are intuitively motivated and fairly easy to compute. Unfortunately, the resulting reduced models need not inherit…

Numerical Analysis · Mathematics 2018-11-26 Mark Embree

An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…

Systems and Control · Electrical Eng. & Systems 2024-08-13 Umair Zulfiqar , Zhi-Hua Xiao , Qiu-Yan Song , Mohammad Monir Uddin , Victor Sreeram

The current study aims to evaluate and investigate the development of projection-based reduced-order models (ROMs) for efficient and accurate RDE simulations. Specifically, we focus on assessing the projection-based ROM construction…

Fluid Dynamics · Physics 2024-08-29 Ryan Camacho , Cheng Huang

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

Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of…

Numerical Analysis · Mathematics 2023-02-17 Ludovica Cicci , Stefania Fresca , Mengwu Guo , Andrea Manzoni , Paolo Zunino

Continuous-time projected dynamical systems are an elementary class of discontinuous dynamical systems with trajectories that remain in a feasible domain by means of projecting outward-pointing vector fields. They are essential when…

Optimization and Control · Mathematics 2020-08-06 Adrian Hauswirth , Saverio Bolognani , Florian Dörfler

Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations, since sufficiently large portions of the bath have to be included in the computation to…

Computational Physics · Physics 2021-09-29 Weiqi Chu , Xiantao Li

We present order reduction results for linear time invariant descriptor systems. Results are given for both forced and unforced systems as well methods for constructing the reduced order systems. Our results establish a precise connection…

Systems and Control · Electrical Eng. & Systems 2021-01-20 Martin Corless , Robert Shorten

It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…

Computational Physics · Physics 2007-05-23 J. M. Aguirregabiria

We propose a novel framework for model-order reduction of hyperbolic differential equations. The approach combines a relaxation formulation of the hyperbolic equations with a discretization using shifted base functions. Model-order…

Numerical Analysis · Mathematics 2021-05-03 Sara Grundel , Michael Herty

Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…

Numerical Analysis · Mathematics 2024-07-17 Julian Koellermeier , Philipp Krah , Jonas Kusch