Chapter 12: Weighted Reduced Order Methods for Uncertainty Quantification

Partial differential equations (PDEs) represent an effective tool to model phenomena in applied sciences. Realistic problems usually depend on several physical and geometrical parameters that can be calibrated exploiting real data. In real scenarios, however, these parameters are affected by uncertainty due to measurement errors or scattered data information. To deal with more reli- able models which take into account this issue, the numerical approximation of stochastic PDEs can be exploited. In the Uncertainty Quantification (UQ) context, many simulations are run to better understand the system at hand and to compute statistics of outcomes over quantities of interest. In particular, the input parameters of the stochastic PDEs are assumed to be random finite–dimensional variables.