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Technical report IES-2013-03. In: Jürgen Beyerer, Alexey Pak (eds.), Proceedings of the 2013 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory, Karlsruher Schriften zur Anthropomatik, vol. 17, KIT Scientific Publishing, 2014.
In many fields, active research is currently focused on quantification and simulation of model uncertainties. The latter are often described probabilistically, allowing for the accurate and detailed answers but necessitating extensive computations. Recently, the generalized polynomial chaos expansion (gPCE) has been proposed as an efficient approach to stochastic computing. In this report, we introduce the mathematical background of gPCE applied to a system described with partial differential equations (PDEs). The potential further benefits of gPCE are discussed and illustrated with synthetic examples.