Name
Abstract | ||
|---|---|---|
We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for truly high-dimensional problems. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jcp.2011.01.002 | J. Comput. Physics |
Keywords | Field | DocType |
uncertainty quantification,measure phenomenon,sparse approximation,high-dimensional problem,stochastic input,empirical correlation,polynomial chaos,compressive sampling,stochastic pde,legacy code,non-adapted sparse approximation,deterministic problem,probabilistic error bound,stochastic coefficient,method converges,black box,convergence in probability,concentration of measure,spectrum | Black box (phreaking),Mathematical optimization,Concentration of measure,Sparse approximation,Polynomial chaos,Sampling (statistics),Probabilistic logic,Partial differential equation,Mathematics,Compressed sensing | Journal |
Volume | Issue | ISSN |
230 | 8 | Journal of Computational Physics |
Citations | PageRank | References |
79 | 3.20 | 34 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alireza Doostan | 1 | 188 | 15.57 |
| Houman Owhadi | 2 | 247 | 21.02 |