Quantification of uncertainties in a distributed parameter system using the generalized polynomial chaos expansion

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.