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Estimating the temperature field of a building envelope could be a time-consuming task. The use of a reduced-order method is then proposed: the Proper Generalized Decomposition method. The solution of the transient heat equation is then…

Computational Engineering, Finance, and Science · Computer Science 2021-11-18 Marie-Hélène Azam , Julien Berger , Sihem Guernouti , Philippe Poullain , Marjorie Musy

The Inertia Relief (IR) technique is widely used by industry and produces equilibrated loads allowing to analyze unconstrained systems without resorting to the more expensive full dynamic analysis. The main goal of this work is to develop a…

Numerical Analysis · Mathematics 2020-12-04 F. Cavaliere , S. Zlotnik , R. Sevilla , X. Larrayoz , P. Diez

Effective models for slender structures derived from well-known plate (or shell) theories are justified within the limit of a small thickness, and may therefore prove limited for intermediate slenderness. On the other hand, direct 3D…

Numerical Analysis · Mathematics 2026-03-30 Jean Ruel , Frédéric Legoll , Arthur Lebée , Ludovic Chamoin

This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework…

Numerical Analysis · Mathematics 2025-10-14 Margarita Chasapi , Pablo Antolin , Annalisa Buffa

We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…

Numerical Analysis · Mathematics 2020-03-23 Ulrich Langer , Andreas Schafelner

Neural networks have proven to be efficient surrogate models for tackling partial differential equations (PDEs). However, their applicability is often confined to specific PDEs under certain constraints, in contrast to classical PDE solvers…

Machine Learning · Computer Science 2023-10-03 Hoyun Choi , Sungyeop Lee , B. Kahng , Junghyo Jo

Determining the proper level of details to develop and solve physical models is usually difficult when one encounters new engineering problems. Such difficulty comes from how to balance the time (simulation cost) and accuracy for the…

Artificial Intelligence · Computer Science 2022-02-03 Randi Wang , Morad Behandish

We introduce a novel Unsmoothed Aggregation (UA) Algebraic Multigrid (AMG) method combined with Preconditioned Conjugate Gradient (PCG) to overcome the limitations of Extended Position-Based Dynamics (XPBD) in high-resolution and…

Graphics · Computer Science 2025-05-20 Chunlei Li , Peng Yu , Tiantian Liu , Siyuan Yu , Yuting Xiao , Shuai Li , Aimin Hao , Yang Gao , Qinping Zhao

This work addresses the accurate and efficient simulation of physical phenomena governed by parametric Partial Differential Equations (PDEs) characterized by varying boundary conditions, where parametric instances modify not only the…

Numerical Analysis · Mathematics 2026-03-10 Francesco Della Santa , Sandra Pieraccini , Maria Strazzullo

A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs,…

Machine Learning · Computer Science 2024-06-28 Alejandro Ribés , Nawfal Benchekroun , Théo Delagnes

In this paper, we present a novel tolerance allocation algorithm for the assessment and control of geometric variation on system performance that is applicable to any system of partial differential equations. In particular, we parameterize…

Numerical Analysis · Mathematics 2019-04-16 Joseph Benzaken , Alireza Doostan , John A. Evans

In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization of domain geometry, then…

Numerical Analysis · Mathematics 2017-10-18 Denis Devaud , Gianluigi Rozza

This work introduces a hybrid approach that combines the Proper Generalised Decomposition (PGD) with deep learning techniques to provide real-time solutions for parametrised mechanics problems. By relying on a tensor decomposition, the…

Computational Physics · Physics 2025-09-03 Alexandre Daby-Seesaram , Kateřina Škardová , Martin Genet

Global aerodynamic design optimization using Euler or Navier-Stokes equations requires very reliable surrogate modeling techniques since the computational effort for the underlying flow simulations is usually high. In general, for such…

Optimization and Control · Mathematics 2018-11-02 Emre Özkaya , Nicolas R. Gauger

Leveraging nonlinear parametrizations for model reduction can overcome the Kolmogorov barrier that affects transport-dominated problems. In this work, we build on the reduced dynamics given by Neural Galerkin schemes and propose to…

Numerical Analysis · Mathematics 2024-12-24 Philipp Weder , Paul Schwerdtner , Benjamin Peherstorfer

A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…

Numerical Analysis · Mathematics 2020-08-28 Giacomo Capodaglio , Marta D'Elia , Max Gunzburger , Pavel Bochev , Manuel Klar , Christian Vollmann

This paper offers an approach to deal with parametrized nonlinear strongly coupled thermo-poroelasticity problems. The approach uses the LATIN-PGD method and extends previous work in multiphysics problems. Proper Generalized Decomposition…

Classical Physics · Physics 2025-08-28 Elise Foulatier , David Néron , François Louf , Pierre-Alain Boucard

Physics-informed neural networks (PINNs) have successfully addressed various computational physics problems based on partial differential equations (PDEs). However, while tackling issues related to irregularities like singularities and…

Machine Learning · Computer Science 2024-11-25 Hang Hu , Sidi Wu , Guoxiong Cai , Na Liu

Surrogate modelling is widely applied in computational science and engineering to mitigate computational efficiency issues for the real-time simulations of complex and large-scale computational models or for many-query scenarios, such as…

Machine Learning · Computer Science 2024-09-26 Konstantinos Kevopoulos , Dongwei Ye

Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…

Numerical Analysis · Mathematics 2021-10-22 Felipe Rocha , Simone Deparis , Pablo Antolin , Annalisa Buffa