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A novel recovery-based error indicator for high-order Finite Difference Methods, based on post-processing of the Finite Difference values is presented. The values obtained on the Finite Difference grid are interpolated into a suitable…

Numerical Analysis · Mathematics 2026-01-19 Ferhat Sindy , Annalisa Buffa , Marco Picasso

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

Optimization and Control · Mathematics 2014-07-30 Matthew J. Zahr , Charbel Farhat

This study proposes a dynamic rule data mining algorithm based on an improved Transformer architecture, aiming to improve the accuracy and efficiency of rule mining in a dynamic data environment. With the increase in data volume and…

Machine Learning · Computer Science 2025-03-17 Jie Liu , Yiwei Zhang , Yuan Sheng , Yujia Lou , Haige Wang , Bohuan Yang

Depending on the frequency range of interest, finite element-based modeling of acoustic problems leads to dynamical systems with very high dimensional state spaces. As these models can mostly be described with second order linear dynamical…

Numerical Analysis · Mathematics 2024-12-17 Siyang Hu , Nick Wulbusch , Alexey Chernov , Tamara Bechtold

This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…

Numerical Analysis · Mathematics 2022-02-24 Georges Semaan , Toni Sayah , Faouzi Triki

We present a novel certified model order reduction (MOR) algorithm for switched descriptor systems applicable to large-scale systems. Our algorithm combines the idea of [Hossain \& Trenn, Technical report, 2023] to reformulate the switched…

Numerical Analysis · Mathematics 2024-04-17 Mattia Manucci , Benjamin Unger

Fully computable a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. To…

Numerical Analysis · Mathematics 2017-07-20 Natalia Kopteva

Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…

Mathematical Physics · Physics 2024-01-03 Alberto Padovan , Blaine Vollmer , Daniel J. Bodony

We present reduced basis approximations and rigorous a posteriori error bounds for the instationary Stokes equations. We shall discuss both a method based on the standard formulation as well as a method based on a penalty approach, which…

Numerical Analysis · Mathematics 2012-11-06 Anna-Lena Gerner , Arnold Reusken , Karen Veroy

Feedback optimization has emerged as an effective strategy for steady-state optimization of dynamical systems. By exploiting models of the steady-state input-output sensitivity, methods of this type are often sample efficient, and their use…

Optimization and Control · Mathematics 2025-09-17 Kristian Lindbäck Løvland , Lars Struen Imsland , Bjarne Grimstad

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…

Computational Engineering, Finance, and Science · Computer Science 2025-04-14 Konstantinos Vlachas , Thomas Simpson , Anthony Garland , D. Dane Quinn , Charbel Farhat , Eleni Chatzi

This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are…

Machine Learning · Statistics 2026-01-05 Shane A. McQuarrie , Mengwu Guo , Anirban Chaudhuri

In this paper we develop two goal-oriented adaptive strategies for a posteriori error estimation within the generalized multiscale finite element framework. In this methodology, one seeks to determine the number of multiscale basis…

Numerical Analysis · Mathematics 2015-09-21 Eric T. Chung , Wing Tat Leung , Sara Pollock

We devise a posteriori error estimators for quasi-optimal nonconforming finite element methods approximating symmetric elliptic problems of second and fourth order. These estimators are defined for all source terms that are admissible to…

Numerical Analysis · Mathematics 2025-02-05 Christian Kreuzer , Matthias Rott , Andreas Veeser , Pietro Zanotti

In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `tweaks' a wide variety of existing post-processing techniques…

Numerical Analysis · Mathematics 2023-03-01 Andreas Dedner , Jan Giesselmann , Tristan Pryer , Jennifer K Ryan

We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…

Numerical Analysis · Mathematics 2026-02-26 Franco Dassi , Rekha Khot , Andres E. Rubiano , Ricardo Ruiz-Baier

The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting non-parametric regression models…

Methodology · Statistics 2018-06-11 Guido Imbens , Stefan Wager

We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity…

Numerical Analysis · Mathematics 2024-06-12 Jan Giesselmann , Kiwoong Kwon

In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…

Systems and Control · Electrical Eng. & Systems 2024-12-20 Maria Cruz Varona , Raphael Gebhart , Julian Suk , Boris Lohmann

We consider the a posteriori error estimation for convection-diffusion-reaction equations in both diffusion-dominated and convection/reaction-dominated regimes. We present an explicit hybrid estimator, which, in each regime, is proved to be…

Numerical Analysis · Mathematics 2021-07-16 Difeng Cai , Zhiqiang Cai
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