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Model order reduction: POD, PGD and reduced bases

Guest Editors: 

  • Francisco Chinesta (PIMM Laboratory, Arts et Métiers Institute of Technology, HESAM Université, Paris, France)
  • Pierre Ladeveze (Université Paris-Saclay, Gif-sur-Yvette, France)
  • Yvon Maday (Université Pierre et Marie Curie, Paris, France) 

This topical issue groups selected research contributions on Model Order Reduction, a new paradigm in the field of simulation-based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies.

Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high-dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real-time simulation, and parametric models. All these problems represent a challenge for standard mesh-based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, real-time optimization, and simulation-based control - critical needs in many branches of science and engineering. Model Order Reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. 

This topical issue addresses mainly model reduction techniques based on the Proper Orthogonal Decomposition, the Proper Generalized Decomposition, and Reduced Basis methodologies.


  1. Standard numerical simulations for optimization or inverse identification of welding processes remain costly and difficult due to their multi-parametric aspect and inherent complexity. The aim of this paper is...

    Authors: Y. Lu, N. Blal and A. Gravouil
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2018 5:3
  2. Many applications are based on the use of materials with heterogeneous microstructure. Prominent examples are fiber-reinforced composites, multi-phase steels or soft tissue to name only a few. The modeling of ...

    Authors: Annika Radermacher, Brett A. Bednarcyk, Bertram Stier, Jaan Simon, Lei Zhou and Stefanie Reese
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:29
  3. In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, a...

    Authors: Filippo Salmoiraghi, Francesco Ballarin, Luca Heltai and Gianluigi Rozza
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:21
  4. Car crash simulations need a lot of computation time. Model reduction can be applied in order to gain time-savings. Due to the highly nonlinear nature of a crash, an automatic separation in parts behaving line...

    Authors: Dennis Grunert and Jörg Fehr
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:20

    The Erratum to this article has been published in Advanced Modeling and Simulation in Engineering Sciences 2016 3:32

  5. Many mechanical experiments in plasticity-induced fatigue are prepared by the recourse to finite element simulations. Usual simulation outputs, like local stress estimations or lifetime predictions, are useful...

    Authors: David Ryckelynck and Djamel Missoum Benziane
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:15
  6. Model order reduction (MOR) methods are more and more applied on many different fields of physics in order to reduce the number of unknowns and thus the computational time of large-scale systems. However, thei...

    Authors: Laurent Montier, Thomas Henneron, Stéphane Clénet and Benjamin Goursaud
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:10
  7. This work presents a data-driven online adaptive model reduction approach for systems that undergo dynamic changes. Classical model reduction constructs a reduced model of a large-scale system in an offline ph...

    Authors: Benjamin Peherstorfer and Karen Willcox
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:11
  8. In this paper, we introduce and comment some recent efficient solvers for time dependent partial differential or ordinary differential problems, considering both linear and nonlinear cases. Here “efficient” ma...

    Authors: Florian De Vuyst
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:8
  9. This paper focuses on the low-dimensional representation of multivariate functions. We study a recursive POD representation, based upon the use of the power iterate algorithm to recursively expand the modes re...

    Authors: M. Azaïez, F. Ben Belgacem and T. Chacón Rebollo
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:3
  10. Inhomogeneous essential boundary conditions must be carefully treated in the formulation of Reduced Order Models (ROMs) for non-linear problems. In order to investigate this issue, two methods are analysed: on...

    Authors: Alejandro Cosimo, Alberto Cardona and Sergio Idelsohn
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:7
  11. Projection-based model order reduction (MOR) using local subspaces is becoming an increasingly important topic in the context of the fast simulation of complex nonlinear models. Most approaches rely on multipl...

    Authors: David Amsallem and Bernard Haasdonk
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:6
  12. Realistic 3D simulations of the tunnelling process are increasingly required to investigate the interactions between machine-driven tunnel construction and the surrounding soil in order to provide reliable est...

    Authors: Ba-Trung Cao, Steffen Freitag and Günther Meschke
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:5
  13. We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutio...

    Authors: Rémi Abgrall, David Amsallem and Roxana Crisovan
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2016 3:1