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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

A systematic approach to nonlinear model order reduction (NMOR) of coupled fluid-structureflight dynamics systems of arbitrary fidelity is presented. The technique employs a Taylor series expansion of the nonlinear residual around…

Computational Engineering, Finance, and Science · Computer Science 2026-04-16 Nikolaos D. Tantaroudas , Ilias Karachalios

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Numerical Analysis · Mathematics 2024-05-15 Nicola Rares Franco , Andrea Manzoni , Paolo Zunino , Jan S. Hesthaven

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

Numerical Analysis · Mathematics 2026-04-27 Dawid Kotowski , Mario Ohlberger

The accuracy of the reduced-order model (ROM) mainly depends on the selected basis. Therefore, it is essential to compute an appropriate basis with an efficient numerical procedure when applying ROM to nonlinear problems. In this paper, we…

Numerical Analysis · Mathematics 2021-05-05 Jun-Geol Ahn , Hyun-Ik Yang , Jin-Gyun Kim

Reduced basis methods are projection-based model order reduction techniques for reducing the computational complexity of solving parametrized partial differential equation problems. In this work we discuss the design of pyMOR, a freely…

Mathematical Software · Computer Science 2019-10-30 René Milk , Stephan Rave , Felix Schindler

We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from…

Numerical Analysis · Mathematics 2020-08-04 Carmen Gräßle , Michael Hinze , Stefan Volkwein

Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for…

Systems and Control · Electrical Eng. & Systems 2025-02-04 Behrad Samari , Amy Nejati , Abolfazl Lavaei

This work presents a nonintrusive physics-preserving method to learn reduced-order models (ROMs) of canonical Hamiltonian systems. Traditional intrusive projection-based model reduction approaches utilize symplectic Galerkin projection to…

Numerical Analysis · Mathematics 2021-12-14 Harsh Sharma , Zhu Wang , Boris Kramer

Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…

Optimization and Control · Mathematics 2024-12-20 Sarah-Alexa Hauschild , Nicole Marheineke , Volker Mehrmann

The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…

Computational Engineering, Finance, and Science · Computer Science 2024-08-23 Lisa Scheunemann , Erik Faust

A comprehensive approach for real-time computations using a database of parameterized linear reduced-order models (ROMs) is proposed. The method proceeds by sampling offline ROMs for specific values of the parameters and interpolating…

Numerical Analysis · Mathematics 2015-06-24 David Amsallem , Radek Tezaur , Charbel Farhat

Projection based model order reduction has become a mature technique for simulation of large classes of parameterized systems. However, several challenges remain for problems where the solution manifold of the parameterized system cannot be…

Numerical Analysis · Mathematics 2022-03-22 Tim Keil , Mario Ohlberger

A data-driven parametric model order reduction (MOR) method using a deep artificial neural network is proposed. The present network, which is the least-squares hierarchical variational autoencoder (LSH-VAE), is capable of performing…

Machine Learning · Computer Science 2023-07-14 SiHun Lee , Sangmin Lee , Kijoo Jang , Haeseong Cho , SangJoon Shin

The Kolmogorov $n$-width of the solution manifolds of transport-dominated problems can decay slowly. As a result, it can be challenging to design efficient and accurate reduced order models (ROMs) for such problems. To address this issue,…

Numerical Analysis · Mathematics 2022-06-29 Zhichao Peng , Min Wang , Fengyan Li

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…

Numerical Analysis · Mathematics 2023-07-10 Jan S. Hesthaven , Cecilia Pagliantini , Nicolò Ripamonti

The increasing size and complexity of modern power systems have led to a high-dimensional mathematical model for transient stability studies, rendering full-scale simulations computationally burdensome. While dimensionality reduction is…

Dynamical Systems · Mathematics 2025-12-08 Farhana Farooq , Danish Rafiq

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Graphics · Computer Science 2025-10-01 Yutian Tao , Maurizio Chiaramonte , Pablo Fernandez

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

The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian…

Numerical Analysis · Mathematics 2017-03-08 Yuezheng Gong , Qi Wang , Zhu Wang