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We introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of…

Numerical Analysis · Mathematics 2022-10-31 Francesca Bonizzoni , Davide Pradovera , Michele Ruggeri

We detail how to use Newton's method for distortion-based curved $r$-adaption to a discrete high-order metric field while matching a target geometry. Specifically, we combine two terms: a distortion measuring the deviation from the target…

Computational Engineering, Finance, and Science · Computer Science 2023-03-22 Guillermo Aparicio-Estrems , Abel Gargallo-Peiró , Xevi Roca

In this study we propose a-posteriori error estimation results to approximate the precision loss in quantities of interests computed using reduced order models. To generate the surrogate models we employ Proper Orthogonal Decomposition and…

Numerical Analysis · Mathematics 2024-12-20 R. Stefanescu , A. Sandu

Conventional offline training of reduced-order bases in a predetermined region of a parameter space leads to parametric reduced-order models that are vulnerable to extrapolation. This vulnerability manifests itself whenever a queried…

Numerical Analysis · Mathematics 2020-04-02 Wanli He , Philip Avery , Charbel Farhat

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

Machine Learning · Computer Science 2026-04-17 Vladimir Fanaskov , Vladislav Trifonov , Alexander Rudikov , Ekaterina Muravleva , Ivan Oseledets

We propose a novel Model Order Reduction framework that is able to handle solutions of hyperbolic problems characterized by multiple travelling discontinuities. By means of an optimization based approach, we introduce suitable calibration…

Numerical Analysis · Mathematics 2025-05-14 Monica Nonino , Davide Torlo

Model Predictive Control (MPC) is a well-established approach to solve infinite horizon optimal control problems. Since optimization over an infinite time horizon is generally infeasible, MPC determines a suboptimal feedback control by…

Optimization and Control · Mathematics 2022-10-26 Saskia Dietze , Martin A. Grepl

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the…

Numerical Analysis · Mathematics 2024-01-22 Anna Ivagnes , Nicola Demo , Gianluigi Rozza

Radial basis functions (RBFs) play an important role in function interpolation, in particular in an arbitrary set of interpolation nodes. The accuracy of the interpolation depends on a parameter called the shape parameter. There are many…

Numerical Analysis · Mathematics 2025-08-27 Maria Han Veiga , Faezeh Nassajian Mojarrad , Fatemeh Nassajian Mojarrad

In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the…

Numerical Analysis · Mathematics 2023-11-21 Nicola Demo , Marco Tezzele , Gianluigi Rozza

In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodology is the use of coarse-proxy models (i.e., lower…

Numerical Analysis · Mathematics 2019-11-14 Philip A. Etter , Yuwei Fan , Lexing Ying

This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…

Machine Learning · Statistics 2019-11-28 Shifeng Xiong

In adaptive control, a controller is precisely designed for a certain model of the system, but that model's parameters are updated online by another mechanism called the adaptive update. This allows the controller to aim for the benefits of…

Systems and Control · Computer Science 2017-11-28 Jason Nezvadovitz

When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct a reduced-order model. Although advances in solving such equations have been made, it is…

Numerical Analysis · Mathematics 2020-03-11 Nguyen Thanh Son , Pierre-Yves Gousenbourger , Estelle Massart , Tatjana Stykel

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 random demodulator is a recent compressive sensing architecture providing efficient sub-Nyquist sampling of sparse band-limited signals. The compressive sensing paradigm requires an accurate model of the analog front-end to enable…

Information Theory · Computer Science 2013-03-26 Pawel Jerzy Pankiewicz , Thomas Arildsen , Torben Larsen

Model order reduction aims to determine a low-order approximation of high-order models with least possible approximation errors. For application to physical systems, it is crucial that the reduced order model (ROM) is robust to any…

Systems and Control · Electrical Eng. & Systems 2025-05-05 Shivam Bajaj , Carolyn L. Beck , Vijay Gupta

We propose a model reduction technique for parametrized partial differential equations arising from scalar hyperbolic conservation laws. The key idea of the technique is to construct basis functions that are local in parameter and time…

Numerical Analysis · Mathematics 2018-05-16 Donsub Rim , Kyle T. Mandli

Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…

Computational Engineering, Finance, and Science · Computer Science 2025-02-26 Abhishek Ajayakumar , Soumyendu Raha

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

Numerical Analysis · Mathematics 2026-04-20 Erik Burman , Mats G. Larson , Karl Larsson , Jonatan Vallin