Name
Title | ||
|---|---|---|
Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification |
Abstract | ||
|---|---|---|
We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantification problem where an assumed probability density on parameters is propagated through the approximate model to produce a probability density, often called a push-forward probability density, on a set of quantities of interest (QoI). The inverse problem considered in this paper seeks to update an initial probability density assumed on model input parameters such that the subsequent push-forward of this updated density through the parameter-to-QoI map matches a given probability density on the QoI. We prove that the densities obtained from solving the forward and inverse problems, using approximate models, converge to the true densities as the approximate models converge to the true models. Numerical results are presented to demonstrate convergence rates of densities for sparse grid approximations of parameter-to-QoI maps and standard spatial and temporal discretizations of PDEs and ODEs. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/18M1181675 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
inverse problems,uncertainty quantification,density estimation,surrogate modeling,response surface approximations,discretization errors | Density estimation,Convergence (routing),Applied mathematics,Uncertainty quantification,Mathematical analysis,Approximations of π,Inverse problem,Probability density function,Sparse grid,Mathematics | Journal |
Volume | Issue | ISSN |
40 | 5 | 1064-8275 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| T Butler | 1 | 27 | 4.27 |
| John D. Jakeman | 2 | 52 | 7.65 |
| Tim Wildey | 3 | 59 | 9.61 |