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- W2913510728 abstract "In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $varrho$. The system's response $f$ pushes forward $varrho$ to a new measure $fcirc varrho$ which we would like to study. However, we might not have access to $f$ but only to its approximation $g$. We thus arrive at a fundamental question -- if $f$ and $g$ are close in $L^q$, does $gcirc varrho$ approximate $fcirc varrho$ well, and in what sense? Previously, we demonstrated that the answer to this question might be negative in terms of the $L^p$ distance between probability density functions (PDF). Here we show that the Wasserstein metric is the proper framework for this question. For any $pgeq 1$, we bound the Wasserstein distance $W_p (fcirc varrho , gcirc varrho) $ from above by $|f-g|_{q}$. Furthermore, we provide lower bounds for the cases of $p=1,2$. Finally, we apply our theory to the analysis of common numerical methods in the field of computational uncertainty quantification." @default.
- W2913510728 created "2019-02-21" @default.
- W2913510728 creator A5031661439 @default.
- W2913510728 date "2019-02-14" @default.
- W2913510728 modified "2023-09-27" @default.
- W2913510728 title "The Wasserstein Distances Between Pushed-Forward Measures with Applications to Uncertainty Quantification" @default.
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