Challenges of order reduction techniques for problems involving polymorphic uncertainty. Issue 2 (15th April 2019)

• Record Type: Journal Article
• Authors: Pivovarov, Dmytro; Willner, Kai; Steinmann, Paul; Brumme, Stephan; Müller, Michael; Srisupattarawanit, Tarin; Ostermeyer, Georg‐Peter; Henning, Carla; Ricken, Tim; Kastian, Steffen; Reese, Stefanie; Moser, Dieter; Grasedyck, Lars; Biehler, Jonas; Pfaller, Martin; Wall, Wolfgang; Kohlsche, Thomas; von Estorff, Otto; Gruhlke, Robert; Eigel, Martin; Ehre, Max; Papaioannou, Iason; Straub, Daniel; Leyendecker, Sigrid
• Other Names: Kaliske Michael guestEditor.; Graf Wolfgang guestEditor.
• Is Part Of: Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik. Volume 42:Issue 2(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-04-15
• Subjects: approximation of uncertain data -- model order reduction -- sensitivity analysis -- surrogate modeling -- uncertainty quantification; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; 510.5
• DOI: 10.1002/gamm.201900011
• Languages: English
• ISSNs: 0936-7195

Abstract

Abstract : Modeling of mechanical systems with uncertainties is extremely challenging and requires a careful analysis of a huge amount of data. Both, probabilistic modeling and nonprobabilistic modeling require either an extremely large ensemble of samples or the introduction of additional dimensions to the problem, thus, resulting also in an enormous computational cost growth. No matter whether the Monte‐Carlo sampling or Smolyak's sparse grids are used, which may theoretically overcome the curse of dimensionality, the system evaluation must be performed at least hundreds of times. This becomes possible only by using reduced order modeling and surrogate modeling. Moreover, special approximation techniques are needed to analyze the input data and to produce a parametric model of the system's uncertainties. In this paper, we describe the main challenges of approximation of uncertain data, order reduction, and surrogate modeling specifically for problems involving polymorphic uncertainty. Thereby some examples are presented to illustrate the challenges and solution methods.