Name
Abstract | ||
|---|---|---|
This paper shows how to systematically and efficiently improve a reduced-order model (ROM) to obtain a better ROM-based estimate of the Conditional Value-at-Risk (CVaR) of a computationally expensive quantity of interest (QoI). Efficiency is gained by exploiting the structure of CVaR, which implies that a ROM used for CVaR estimation only needs to be accurate in a small region of the parameter space, called the epsilon-risk region. Hence, any full-order model (FOM) queries needed to improve the ROM can be restricted to this small region of the parameter space, thereby substantially reducing the computational cost of ROM construction. However, an example is presented which shows that simply constructing a new ROM that has a smaller error with the FOM is in general not sufficient to yield a better CVaR estimate. Instead a combination of previous ROMs is proposed that achieves a guaranteed improvement, as well as c-risk regions that converge monotonically to the FOM risk region with decreasing ROM error. Error estimates for the ROM-based CVaR estimates are presented. The gains in efficiency obtained by improving a ROM only in the small epsilon-risk region over a traditional greedy procedure on the entire parameter space are illustrated numerically. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1137/19M1257433 | SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION |
Keywords | DocType | Volume |
reduced-order models,risk measures,Conditional Value-at-Risk,estimation,sampling,uncertainty quantification | Journal | 8 |
Issue | ISSN | Citations |
2 | 2166-2525 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Matthias Heinkenschloss | 1 | 186 | 24.70 |
| Boris Kramer | 2 | 6 | 4.19 |
| Timur Takhtaganov | 3 | 0 | 0.34 |