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Computing the statistical properties of nonlinear random systems is of fundamental importance in many areas of science and engineering. The primary objective of the course is to introduce students to state-of-the-art methods for uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in in dealing with systems specified in terms of stochastic ordinary and partial differential equations. Topics covered include: polynomial chaos methods (gPC and ME-gPC), probabilistic collocation methods (PCM and ME-PCM), Monte-Carlo methods (MC, quasi-MC, multi-level MC), sparse grids (SG), probability density function methods, and techniques for dimensional reduction. Basic knowledge of probability theory and elementary numerical methods for ODEs and PDEs is recommended.
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