English
Related papers

Related papers: E2N: Error Estimation Networks for Goal-Oriented M…

200 papers

Recent research increasingly integrates machine learning (ML) into predictive maintenance (PdM) to reduce operational and maintenance costs in data-rich operational settings. However, uncertainty due to model misspecification continues to…

Artificial Intelligence · Computer Science 2025-06-25 Zhuojun Xie , Adam Abdin , Yiping Fang

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

Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces…

Machine Learning · Computer Science 2025-10-01 Zhizhou Zhang , Youjia Wu , Kaixuan Zhang , Yanjia Wang

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…

Optimization and Control · Mathematics 2021-06-18 Caroline Geiersbach , Winnifried Wollner

Defeaturing, the process of simplifying computational geometries, is a critical step in industrial simulation pipelines for reducing computational cost. Rigorous a posteriori estimators exist for the global energy-norm error introduced by…

Numerical Analysis · Mathematics 2025-12-24 Philipp Weder , Annalisa Buffa

The development of QoE models by means of Machine Learning (ML) is challenging, amongst others due to small-size datasets, lack of diversity in user profiles in the source domain, and too much diversity in the target domains of QoE models.…

Computer Vision and Pattern Recognition · Computer Science 2020-03-20 Selim Ickin , Markus Fiedler , Konstantinos Vandikas

We consider goal-oriented adaptive space-time finite-element discretizations of the parabolic heat equation on completely unstructured simplicial space-time meshes. In some applications, we are interested in an accurate computation of some…

Numerical Analysis · Mathematics 2024-01-31 Bernhard Endtmayer , Andreas Schafelner

When numerically solving partial differential equations, for a given problem and operating condition, adaptive mesh refinement (AMR) has proven its efficiency to automatically build a discretization achieving a prescribed accuracy at low…

Adaptive finite element methods are a powerful tool to obtain numerical simulation results in a reasonable time. Due to complex chemical and mechanical couplings in lithium-ion batteries, numerical simulations are very helpful to…

Numerical Analysis · Mathematics 2024-04-17 Raphael Schoof , Lennart Flür , Florian Tuschner , Willy Dörfler

We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…

Numerical Analysis · Mathematics 2015-06-22 A. Johansson , J. H. Chaudry , V. Carey , D. Estep , V. Ginting , M. Larson , S. Tavener

In this article, goal-oriented a posteriori error estimation for the biharmonic plate bending problem is considered. The error for approximation of goal functional is represented by an estimator which combines dual-weighted residual method…

Numerical Analysis · Mathematics 2021-07-15 Gouranga Mallik

The simulation of complex nonlinear engineering systems such as compressible fluid flows may be targeted to make more efficient and accurate the approximation of a specific (scalar) quantity of interest of the system. Putting aside modeling…

Numerical Analysis · Mathematics 2018-11-14 Jan Van Langenhove , Didier Lucor , Frédéric Alauzet , Anca Belme

We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algorithm to compute a quantity of interest to a given tolerance…

Numerical Analysis · Mathematics 2007-08-02 Marcel Arndt , Mitchell Luskin

The rapidly growing traffic demands in fiber-optical networks require flexibility and accuracy in configuring lightpaths, for which fast and accurate quality of transmission (QoT) estimation is of pivotal importance. This paper introduces a…

Networking and Internet Architecture · Computer Science 2023-05-15 Jasper Müller , Sai Kireet Patri , Tobias Fehenberger , Helmut Griesser , Jörg-Peter Elbers , Carmen Mas-Machuca

Deep learning (DL) based channel estimation (CE) and multiple input and multiple output detection (MIMODet), as two separate research topics, have provided convinced evidence to demonstrate the effectiveness and robustness of artificial…

Signal Processing · Electrical Eng. & Systems 2024-01-30 Xiangzhao Qin , Sha Hu , Jiankun Zhang , Jing Qian , Hao Wang

Using simulation to predict the mechanical behavior of heterogeneous materials has applications ranging from topology optimization to multi-scale structural analysis. However, full-fidelity simulation techniques such as Finite Element…

Machine Learning · Computer Science 2021-10-26 S. Mohammadzadeh , E. Lejeune

Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…

Graphics · Computer Science 2026-02-13 Zhiyuan Zhang , Amir Vaxman , Stefanos-Aldo Papanicolopulos , Kartic Subr

We study adaptive mesh selection for the solution of systems of initial value problems. The goal is a rigorous theoretical analysis of potential advantages of adaption. For an optimal method in the sense of the speed of convergence, we…

Numerical Analysis · Mathematics 2018-11-12 Boleslaw Kacewicz

In this paper, we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations (PDEs). The main idea is to use a neural network to learn the…

Numerical Analysis · Mathematics 2024-10-11 Shukai Du , Samuel N. Stechmann

The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…

Numerical Analysis · Mathematics 2023-09-18 Philipp Bringmann