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This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominated problems with limited training. The proposed approach…

Numerical Analysis · Mathematics 2023-09-14 Marzieh Alireza Mirhoseini , Matthew J. Zahr

In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…

Numerical Analysis · Mathematics 2024-01-22 Maria Strazzullo , Fabio Vicini

Online adaptive model reduction efficiently reduces numerical models of transport-dominated problems by updating reduced spaces over time, which leads to nonlinear approximations on latent manifolds that can achieve a faster error decay…

Numerical Analysis · Mathematics 2023-07-28 Rodrigo Singh , Wayne Isaac Tan Uy , Benjamin Peherstorfer

This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We…

Computer Vision and Pattern Recognition · Computer Science 2011-12-20 Vijayaraghavan Thirumalai , Pascal Frossard

Model order reduction seeks to approximate large-scale dynamical systems by lower-dimensional reduced models. For linear systems, a small reduced dimension directly translates into low computational cost, ensuring online efficiency. This…

Numerical Analysis · Mathematics 2025-12-17 Björn Liljegren-Sailer

We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…

Numerical Analysis · Mathematics 2016-09-21 Sebastian Ullmann , Marko Rotkvic , Jens Lang

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

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 present work considers the optimal control of a convective Cahn-Hilliard system, where the control enters through the velocity in the transport term. We prove the existence of a solution to the considered optimal control problem. For an…

Optimization and Control · Mathematics 2018-03-08 Carmen Gräßle , Michael Hinze , Nicolas Scharmacher

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…

Numerical Analysis · Mathematics 2019-10-04 Youngsoo Choi , Peter Brown , Bill Arrighi , Robert Anderson

Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…

Numerical Analysis · Mathematics 2026-03-27 Lijie Ji , Sabrina Rashid , Yanlai Chen , Zhu Wang

We present a data-driven nonintrusive model order reduction method for dynamical systems with moving boundaries. The proposed method draws on the proper orthogonal decomposition, Gaussian process regression, and moving least squares…

Computational Engineering, Finance, and Science · Computer Science 2021-03-18 Zhan Ma , Wenxiao Pan

Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…

Numerical Analysis · Mathematics 2018-11-21 Gianluigi Rozza , Haris Malik , Nicola Demo , Marco Tezzele , Michele Girfoglio , Giovanni Stabile , Andrea Mola

This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear…

Computer Vision and Pattern Recognition · Computer Science 2015-06-03 Vijayaraghavan Thirumalai , Pascal Frossard

In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality…

Machine Learning · Statistics 2023-11-01 Wenwu Gong , Zhejun Huang , Lili Yang

To describe non-equilibrium transport processes in a quantum device with infinite baths, we propose to formulate the problems as a reduced-order problem. Starting with the Liouville-von Neumann equation for the density-matrix, the…

Mesoscale and Nanoscale Physics · Physics 2019-11-04 Weiqi Chu , Xiantao Li

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

Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfaces. Developing model reduction methods for computational…

Computational Physics · Physics 2014-07-09 Maciej Balajewicz , Charbel Farhat

Several reduced order models have been developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction…

Numerical Analysis · Computer Science 2020-01-06 Youngsoo Choi , Deshawn Coombs , Robert Anderson

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

Machine Learning · Statistics 2025-02-20 Patrick Héas , Cédric Herzet , Benoit Combès