Name
Abstract | ||
|---|---|---|
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard ℓ1-minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients, when available, and refer to the resulting algorithm as weighted ℓ1-minimization. We provide conditions under which we may guarantee recovery using this weighted scheme. Numerical tests are used to compare the weighted and non-weighted methods for the recovery of solutions to two differential equations with high-dimensional random inputs: a boundary value problem with a random elliptic operator and a 2-D thermally driven cavity flow with random boundary condition. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.jcp.2014.02.024 | Journal of Computational Physics |
Keywords | DocType | Volume |
Compressive sampling,Sparse approximation,Polynomial chaos,Basis pursuit denoising (BPDN),Weighted ℓ1-minimization,Uncertainty quantification,Stochastic PDEs | Journal | 267 |
ISSN | Citations | PageRank |
0021-9991 | 27 | 1.02 |
References | Authors | |
25 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ji Peng | 1 | 27 | 1.36 |
| Jerrad Hampton | 2 | 31 | 2.74 |
| Alireza Doostan | 3 | 188 | 15.57 |