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Surrogate neural network-based partial differential equation (PDE) solvers have the potential to solve PDEs in an accelerated manner, but they are largely limited to systems featuring fixed domain sizes, geometric layouts, and boundary…

Machine Learning · Computer Science 2025-01-10 Chenkai Mao , Robert Lupoiu , Tianxiang Dai , Mingkun Chen , Jonathan A. Fan

Modern generations of field-programmable gate arrays (FPGAs) allow for partial reconfiguration. In an online context, where the sequence of modules to be loaded on the FPGA is unknown beforehand, repeated insertion and deletion of modules…

Hardware Architecture · Computer Science 2007-05-23 Jan van der Veen , Sandor P. Fekete , Ali Ahmadinia , Christophe Bobda , Frank Hannig , Juergen Teich

We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order…

Numerical Analysis · Mathematics 2022-02-22 Kathrin Smetana , Tommaso Taddei

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

Machine Learning · Computer Science 2023-12-18 Raphaël Pestourie , Youssef Mroueh , Chris Rackauckas , Payel Das , Steven G. Johnson

Solving and optimising Partial Differential Equations (PDEs) in geometrically parameterised domains often requires iterative methods, leading to high computational and time complexities. One potential solution is to learn a direct mapping…

Numerical Analysis · Mathematics 2025-06-12 Guglielmo Padula , Gianluigi Rozza

We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…

Numerical Analysis · Mathematics 2025-10-30 Abbas Kabalan , Fabien Casenave , Felipe Bordeu , Virginie Ehrlacher , Alexandre Ern

A novel refinement measure for non-intrusive surrogate modelling of partial differential equations (PDEs) with uncertain parameters is proposed. Our approach uses an empirical interpolation procedure, where the proposed refinement measure…

Numerical Analysis · Mathematics 2019-07-10 Yous van Halder , Benjamin Sanderse , Barry Koren

Current simulation of metal forging processes use advanced finite element methods. Such methods consist of solving mathematical equations, which takes a significant amount of time for the simulation to complete. Computational time can be…

Numerical Analysis · Mathematics 2023-03-20 Meduri Venkata Shivaditya , José Alves , Francesca Bugiotti , Frederic Magoules

The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…

Numerical Analysis · Mathematics 2022-10-26 Petr N. Vabishchevich

Gradient-based optimization of engineering designs is limited by non-differentiable components in the typical computer-aided engineering (CAE) workflow, which calculates performance metrics from design parameters. While gradient-based…

Computational Engineering, Finance, and Science · Computer Science 2025-11-17 Andrin Rehmann , Nolan Black , Josiah Bjorgaard , Alessandro Angioi , Andrei Paleyes , Niklas Heim , Dion Häfner , Alexander Lavin

Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many…

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 present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…

Numerical Analysis · Mathematics 2020-07-24 Mehdi Elasmi , Christoph Erath , Stefan Kurz

Simulation techniques such as the finite element method are essential for designing electrical devices, but their computational cost can be prohibitive for repeated or real-time computations. Projection-based model order reduction…

Computational Engineering, Finance, and Science · Computer Science 2026-01-27 Matteo Zorzetto , Merle Backmeyer , Michael Wiesheu , Riccardo Torchio , Fabrizio Dughiero , Sebastian Schöps

Offline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact…

Numerical Analysis · Mathematics 2015-04-20 Eric T. Chung , Yalchin Efendiev , Wing Tat Leung

We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal…

Numerical Analysis · Mathematics 2019-03-07 Ulrich Langer , Andreas Schafelner

A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interface conditions, is presented and analysed. The study of…

Numerical Analysis · Mathematics 2013-04-16 Andrea Cangiani , Emmanuil H. Georgoulis , Max Jensen

A novel domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) model-reduction method applicable to parameterized systems of nonlinear algebraic equations (e.g., arising from discretizing a parameterized partial-differential-equations…

Numerical Analysis · Mathematics 2021-07-07 Chi Hoang , Youngsoo Choi , Kevin Carlberg

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…

Numerical Analysis · Mathematics 2021-10-18 Zhongjian Wang , Wenlong Zhang , Zhiwen Zhang

Many imaging problems require computing spatial transformations induced by spatially varying intensity, feature, or density fields. Canonical examples include distortion correction, deformable image registration, atlas-based segmentation,…

Computer Vision and Pattern Recognition · Computer Science 2026-05-29 Yanwen Huang , Lok Ming Lui , Gary P. T. Choi