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A promising approach to investigating high-dimensional problems is to identify their intrinsically low-dimensional features, which can be achieved through recently developed techniques for effective low-dimensional representation of…

Analysis of PDEs · Mathematics 2025-06-02 Zeyu Jin , Ruo Li

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

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…

Fluid Dynamics · Physics 2020-06-10 Nirmal J. Nair , Andres Goza

The paper presents a Projection-Based Reduced-Order Model for simulations of high Reynolds turbulent flows. The PBROM are enhanced by incorporating various models of turbulent viscosity and residual closures to model the effects of…

Computational Engineering, Finance, and Science · Computer Science 2021-05-25 My Ha Dao , Hoang Huy Nguyen

Nonlinear systems exist widely in nature, however, how to construct systems with accurate expected non-linearity artificially is still a problem, which greatly limits their experimental study and engineering application. In this paper, we…

Dynamical Systems · Mathematics 2023-03-10 Qiangqiang Li , Qingjie Cao

Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which…

Numerical Analysis · Mathematics 2024-04-03 Patrick Buchfink , Silke Glas , Bernard Haasdonk , Benjamin Unger

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…

Optimization and Control · Mathematics 2011-06-15 Jake Bouvrie , Boumediene Hamzi

A reduced order model of a generic submarine is presented. Computational fluid dynamics (CFD) results are used to create and validate a model that includes depth dependence and the effect of waves on the craft. The model and the procedure…

Systems and Control · Electrical Eng. & Systems 2022-12-21 J. Ezequiel Martin , Maxwell Hammond , Nicholas Rober , Yakin Kim , Venanzio Cichella , Pablo Carrica

Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…

Optimization and Control · Mathematics 2022-01-17 Samuel E. Otto , Alberto Padovan , Clarence W. Rowley

This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…

Numerical Analysis · Computer Science 2018-07-04 Kevin Carlberg , Youngsoo Choi , Syuzanna Sargsyan

Two moment-matching methods for model reduction of linear switched systems (LSSs) are presented. The methods are similar to the Krylov subspace methods used for moment matching for linear systems. The more general one of the two methods, is…

Systems and Control · Computer Science 2016-11-15 Mert Bastug , Mihaly Petreczky , Rafael Wisniewski , John Leth

In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…

Numerical Analysis · Mathematics 2026-04-13 Elise Bonnet-Weill , Virginie Ehrlacher , Luca Nenna

Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…

Dynamical Systems · Mathematics 2022-10-03 Peter Benner , Pawan Goyal , Jan Heiland , Igor Pontes

Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for…

Mathematical Physics · Physics 2019-10-23 Oğul Esen , Manuel de León , Víctor Manuel Jiménez Morales , Cristina Sardón

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

Fluid Dynamics · Physics 2020-04-13 Ali Thari , Vito Pasquariello , Niels Aage , Stefan Hickel

We present an exact dimensional reduction for high-dimensional dynamical systems composed of $N$ identical dynamical units governed by quasi-linear ordinary differential equations (ODEs) of order $M$. In these systems, each unit follows a…

Adaptation and Self-Organizing Systems · Physics 2026-05-15 Felix Augustsson , Erik Andreas Martens , Rok Cestnik

We consider model order reduction for a free boundary problem of an osmotic cell that is parameterized by material parameters as well as the initial shape of the cell. Our approach is based on an Arbitrary-Lagrangian-Eulerian description of…

Numerical Analysis · Mathematics 2021-06-09 Christoph Lehrenfeld , Stephan Rave

Lyapunov-Schmidt reduction is a dimensionality reduction technique in nonlinear systems analysis that is commonly utilised in the study of bifurcation problems in high-dimensional systems. The method is a systematic procedure for reducing…

Systems and Control · Electrical Eng. & Systems 2024-09-16 Pranav Gupta , Anastasia Bizyaeva , Ravi Banavar

In this work, we present a reduced-order model for a nonlinear cross-diffusion problem from population dynamics, for the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volterra kinetics. The finite-difference discretization of the…

Numerical Analysis · Mathematics 2021-03-04 Bülent Karasözen , Gülden Mülayim , Murat Uzunca , Süleyman Yıldız

In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form.…

Numerical Analysis · Mathematics 2023-07-19 Süleyman Yıldız , Murat Uzunca , Bülent Karasözen