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Challenges of order reduction techniques for problems involving polymorphic uncertainty
Author(s) -
Pivovarov Dmytro,
Willner Kai,
Steinmann Paul,
Brumme Stephan,
Müller Michael,
Srisupattarawanit Tarin,
Ostermeyer GeorgPeter,
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
Publication year - 2019
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201900011
Subject(s) - uncertainty quantification , computer science , monte carlo method , dimensionality reduction , reduction (mathematics) , curse of dimensionality , parametric statistics , probabilistic logic , model order reduction , surrogate model , sparse grid , mathematical optimization , sampling (signal processing) , uncertainty reduction theory , uncertainty analysis , algorithm , machine learning , artificial intelligence , mathematics , simulation , statistics , projection (relational algebra) , geometry , filter (signal processing) , computer vision , communication , sociology
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.