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Iterative Krylov projection methods have become widely used for solving large-scale linear inverse problems. However, methods based on orthogonality include the computation of inner-products, which become costly when the number of…

Numerical Analysis · Mathematics 2025-02-06 Malena Sabaté Landman , Ariana N. Brown , Julianne Chung , James G. Nagy

Model-order reduction techniques allow the construction of low-dimensional surrogate models that can accelerate engineering design processes. Often, these techniques are intrusive, meaning that they require direct access to underlying…

Dynamical Systems · Mathematics 2023-08-16 Yevgeniya Filanova , Igor Pontes Duff , Pawan Goyal , Peter Benner

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

This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the…

Numerical Analysis · Mathematics 2021-08-23 Julianne Chung , Silvia Gazzola

This article deals with the efficient and certified numerical approximation of the smallest eigenvalue and the associated eigenspace of a large-scale parametric Hermitian matrix. For this aim, we rely on projection-based model order…

Numerical Analysis · Mathematics 2026-01-14 Mattia Manucci , Benjamin Stamm , Zhuoyao Zeng

In this paper, an $\mathscr{H}_2$ norm-based model reduction method for linear quantum systems is presented, which can obtain a physically realizable model with a reduced order for closely approximating the original system. The model…

Quantum Physics · Physics 2024-11-21 G. P. Wu , S. Xue , G. F. Zhang , I. R. Petersen

In this paper, we present an adaptive framework for constructing a pseudo-optimal reduced model for the frequency-limited H2-optimal model order reduction problem. We show that the frequency-limited pseudo-optimal reduced-order model has an…

Systems and Control · Electrical Eng. & Systems 2021-09-27 Umair Zulfiqar , Victor Sreeram , Xin Du

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

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

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…

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

To fully exploit the capabilities of next-generation gravitational wave detectors, we need to significantly improve the accuracy of our models of gravitational-wave-emitting systems. This paper focuses on one way of doing so: by taking…

General Relativity and Quantum Cosmology · Physics 2023-06-07 Andrew Spiers , Adam Pound , Jordan Moxon

We investigate the optimal model reduction problem for large-scale quadratic-bilinear (QB) control systems. Our contributions are threefold. First, we discuss the variational analysis and the Volterra series formulation for QB systems. We…

Numerical Analysis · Mathematics 2017-05-17 Peter Benner , Pawan Goyal , Serkan Gugercin

Parametric high-fidelity simulations are of interest for a wide range of applications. But the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order…

Numerical Analysis · Mathematics 2019-02-28 Patrick Buchfink , Ashish Bhatt , Bernard Haasdonk

We investigate linear dynamical systems of second order. Uncertainty quantification is applied, where physical parameters are substituted by random variables. A stochastic Galerkin method yields a linear dynamical system of second order…

Numerical Analysis · Mathematics 2023-06-21 Roland Pulch

Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of non-parametric linear time-invariant (LTI) systems are known and well-investigated. In this work, using the general framework of…

Optimization and Control · Mathematics 2024-11-12 Petar Mlinarić , Peter Benner , Serkan Gugercin

Low-Rank Adaptation (LoRA) enables efficient fine-tuning of large language models but suffers from catastrophic forgetting when learned updates interfere with the dominant singular directions that encode essential pre-trained knowledge. We…

Computation and Language · Computer Science 2025-11-11 Yifeng Xiong , Xiaohui Xie

The frequency-weighted model order reduction techniques are used to find a lower-order approximation of the high-order system that exhibits high-fidelity within the frequency region emphasized by the frequency weights. In this paper, we…

Systems and Control · Electrical Eng. & Systems 2020-11-20 Umair Zulfiqar , Victor Sreeram , Mian Ilyas Ahmad , Xin Du

We propose a model order reduction framework for incompressible fluid-structure interaction (FSI) problems based on high-order implicit Runge-Kutta (IRK) methods. We consider separate reduced spaces for fluid velocity, fluid pressure and…

Numerical Analysis · Mathematics 2025-12-30 Tommaso Taddei , Xuejun Xu , Lei Zhang

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