Challenges of order reduction techniques for problems involving polymorphic uncertainty

Journal article

Publication Details

Author(s): Pivovarov D, Willner K, Steinmann P, Brumme S, Müller M, Srisupattarawanit T, Ostermeyer GP, Henning C, Ricken T, Kastian S, Reese S, Moser D, Grasedyck L, Biehler J, Pfaller M, Wall W, Kohlsche T, Estorff Ov, Gruhlke R, Eigel M, Ehre M, Papaioannou I, Straub D, Leyendecker S
Journal: GAMM-Mitteilungen
Publication year: 2019
ISSN: 0936-7195
eISSN: 1522-2608


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.

FAU Authors / FAU Editors

Leyendecker, Sigrid Prof. Dr.-Ing.
Chair of Applied Dynamics
Pivovarov, Dmytro
Lehrstuhl für Technische Mechanik
Steinmann, Paul Prof. Dr.-Ing.
Lehrstuhl für Technische Mechanik
Willner, Kai Prof. Dr.-Ing.
Professur für Strukturmechanik

External institutions
Deutsches Konsortium für Translationale Krebsforschung (DKTK) Deutsches Krebsforschungszentrum
Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen
Technische Universität Braunschweig
Technische Universität Hamburg-Harburg (TUHH)
Universität Stuttgart
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) - Leibniz-Institut im Forschungsverbund Berlin e. V.

How to cite

Pivovarov, D., Willner, K., Steinmann, P., Brumme, S., Müller, M., Srisupattarawanit, T.,... Leyendecker, S. (2019). Challenges of order reduction techniques for problems involving polymorphic uncertainty. GAMM-Mitteilungen.

Pivovarov, Dmytro, et al. "Challenges of order reduction techniques for problems involving polymorphic uncertainty." GAMM-Mitteilungen (2019).


Last updated on 2019-23-05 at 08:23