Name
Title | ||
|---|---|---|
Practical error bounds for a non-intrusive bi-fidelity approach to parametric/stochastic model reduction. |
Abstract | ||
|---|---|---|
For practical model-based demands, such as design space exploration and uncertainty quantification (UQ), a high-fidelity model that produces accurate outputs often has high computational cost, while a low-fidelity model with less accurate outputs has low computational cost. It is often possible to construct a bi-fidelity model having accuracy comparable with the high-fidelity model and computational cost comparable with the low-fidelity model. This work presents the construction and analysis of a non-intrusive (i.e., sample-based) bi-fidelity model that relies on the low-rank structure of the map between model parameters/uncertain inputs and the solution of interest, if exists. Specifically, we derive a novel, pragmatic estimate for the error committed by this bi-fidelity model. We show that this error bound can be used to determine if a given pair of low- and high-fidelity models will lead to an accurate bi-fidelity approximation. The cost of this error bound is relatively small and depends on the solution rank. The value of this error estimate is demonstrated using two example problems in the context of UQ, involving linear and non-linear partial differential equations. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.jcp.2018.04.015 | Journal of Computational Physics |
Keywords | Field | DocType |
Matrix interpolative decomposition,Uncertainty quantification,Low-rank approximation,Multi-fidelity approximation,Bi-fidelity approximation,Parametric model reduction | Mathematical optimization,Fidelity,Uncertainty quantification,Parametric statistics,Stochastic modelling,Partial differential equation,Design space exploration,Mathematics | Journal |
Volume | ISSN | Citations |
368 | 0021-9991 | 1 |
PageRank | References | Authors |
0.37 | 15 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jerrad Hampton | 1 | 31 | 2.74 |
| Hillary R. Fairbanks | 2 | 3 | 0.77 |
| Akil Narayan | 3 | 77 | 12.59 |
| Alireza Doostan | 4 | 188 | 15.57 |