Weighted Reduced Order Methods for Uncertainty Quantification
Published in Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics, chapter 12, pages 251-264. Society for Industrial & Applied Mathematics, U.S., 2022
Recommended citation: Davide Torlo, Maria Strazzullo, Francesco Ballarin, and Gianluigi Rozza. Weighted reduced order methods for uncertainty quantification. In Francesco Ballarin Gianluigi Rozza, Giovanni Stabile, editor, Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics, chapter 12, pages 251-264. Society for Industrial & Applied Mathematics, U.S., 2022. https://doi.org/10.1137/1.9781611977257.ch12 https://doi.org/10.1137/1.9781611977257.ch12
Partial differential equations (PDEs) are an effective tool to model phenomena in applied sciences. Realistic problems usually depend on several physical and geometrical parameters that can be calibrated by using real data. In real scenarios, however, these parameters are affected by uncertainty due to measurement errors or scattered data information. To deal with more reliable models which take this issue into account, stochastic PDEs can be numerically approximated. 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.
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