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A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing…

Numerical Analysis · Mathematics 2017-02-01 Pia Domschke , Aseem Dua , Jeroen J. Stolwijk , Jens Lang , Volker Mehrmann

This study proposes an adaptive data-driven hyperparameter tuning framework for black-box 3D LiDAR odometry algorithms. The proposed framework comprises offline parameter-error function modeling and online adaptive parameter selection. In…

Robotics · Computer Science 2021-07-12 Kenji Koide , Masashi Yokozuka , Shuji Oishi , Atsuhiko Banno

In this work, we present a model order reduction technique for nonlinear structures assembled from components.The reduced order model is constructed by reducing the substructures with proper orthogonal decomposition and connecting them by a…

Computational Engineering, Finance, and Science · Computer Science 2024-11-15 Stephan Ritzert , Jannick Kehls , Stefanie Reese , Tim Brepols

This paper proposes and tests the first-ever reduced basis warm-start iterative method for the parametrized linear systems, exemplified by those discretizing the parametric partial differential equations. Traditional iterative methods are…

Numerical Analysis · Mathematics 2024-01-08 Shijin Hou , Yanlai Chen , Yinhua Xia

In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high…

Numerical Analysis · Mathematics 2015-05-20 Assyr Abdulle , Patrick Henning

We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits…

Numerical Analysis · Mathematics 2023-01-24 Sridhar Chellappa , Lihong Feng , Peter Benner

We consider parameter identification problems in parametrized partial differential equations (PDE). This leads to nonlinear ill-posed inverse problems. One way to solve them are iterative regularization methods, which typically require…

Numerical Analysis · Mathematics 2018-05-07 Dominik Garmatter , Bernard Haasdonk , Bastian Harrach

Subset selection for the rank $k$ approximation of an $n\times d$ matrix $A$ offers improvements in the interpretability of matrices, as well as a variety of computational savings. This problem is well-understood when the error measure is…

Data Structures and Algorithms · Computer Science 2023-04-20 David P. Woodruff , Taisuke Yasuda

This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…

Numerical Analysis · Mathematics 2016-11-23 E. H. van Brummelen , S. Zhuk , G. J. van Zwieten

We present a one-dimensional shear-force-driven droplet formation model with a flux-based error estimator. The model is derived using asymptotic expansion and a front-tracking method to simulate the droplet interface. The model is then…

Numerical Analysis · Mathematics 2026-05-25 Darsh Nathawani , Matthew Knepley

We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…

Numerical Analysis · Mathematics 2014-11-03 Paul G. Constantine , David F. Gleich , Yangyang Hou , Jeremy Templeton

Modern applications in sensitive domains such as biometrics and medicine frequently require the use of non-decomposable loss functions such as precision@k, F-measure etc. Compared to point loss functions such as hinge-loss, these offer much…

Machine Learning · Computer Science 2014-10-27 Purushottam Kar , Harikrishna Narasimhan , Prateek Jain

The Reduced Basis Method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the \textit{offline} portion of the algorithm is a greedy algorithm, requiring…

Numerical Analysis · Mathematics 2017-03-17 Jiahua Jiang , Yanlai Chen , Akil Narayan

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

Numerical Analysis · Mathematics 2024-03-20 Janina E. Schütte , Martin Eigel

In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…

Optimization and Control · Mathematics 2019-05-21 I. Necoara , T. C. Ionescu

In this work, we propose a framework that constructs reduced order models for nonlinear structural mechanics in a nonintrusive fashion, and can handle large scale simulations. We identify three steps that are carried out separately in time,…

Numerical Analysis · Mathematics 2023-02-02 Fabien Casenave , Nissrine Akkari , Felipe Bordeu , Christian Rey , David Ryckelynck

It is crucially important to estimate unknown parameters in earth system models by integrating observation and numerical simulation. For many applications in earth system sciences, an optimization method which allows parameters to…

Geophysics · Physics 2022-07-13 Yohei Sawada

In this paper, we develop and analyze an adaptive multiscale approach for heterogeneous problems in perforated domains. In many applications, these problems have a multiscale nature arising because of the perforations, their geometries, the…

Numerical Analysis · Mathematics 2016-05-26 Eric T. Chung , Yalchin Efendiev , Wing Tat Leung , Maria Vasilyeva , Yating Wang

We study online learning in the random-order model, where the multiset of loss functions is chosen adversarially but revealed in a uniformly random order. By extending the batch-to-online transformation of Dong and Yoshida (2023), we show…

Machine Learning · Statistics 2026-05-11 Shinsaku Sakaue , Yuichi Yoshida

For the non-conforming Crouzeix-Raviart boundary elements from [Heuer, Sayas: Crouzeix-Raviart boundary elements, Numer. Math. 112, 2009], we develop and analyze a posteriori error estimators based on the $h-h/2$ methodology. We discuss the…

Numerical Analysis · Mathematics 2013-12-03 Norbert Heuer , Michael Karkulik