Supporting Smith: Section 11.1.2 (Tensor product formulation)
Corrections/Notes/FAQs:
- None
Stochastic polynomial methods were unreasonably effective for uncertainty propatation with one uncertain input (the 1d case). We now consider the (much more likely) case that we have a large number of uncertain inputs of our model, which uncertainties will combine and interact to produce significant uncertainty in output quantities of interest.
Again we focus on the question of obtaining statistical moments of the output, given complete knowledge of the input distributions (we know moments, pdf, samples, whatever we want). We look for means of combining 1d rules to obtain n-d rules. We consider the tensor-product option, which shows very poor scaling as dimension increases. This motivates the discussion of an alternative: sparse grids.
Recommended supportive reading is Chapter 11 of Smith. After these videos, you should be able to attempt Tutorial 2.
Supporting Smith: Section 11.1.2 (Tensor product formulation)
Corrections/Notes/FAQs:
Supporting Smith: Section 11.1.2 (Tensor product formulation)
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Supporting Smith: Section 11.1.2 (Nested quadrature techniques)
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Supporting Smith: Section 11.1.3
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Supporting Smith: Section 11.1.3
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Total time: 1:53:30
dr. R. Dwight ≤r.p.dwight@tudelft.nl≥ - 2022-04-05
