Sparse approximation of multilinear problems with applications to kernel-based methods in UQ

作者：Nobile Fabio; Tempone Raul; Wolfers Soren^*

来源：Numerische Mathematik, 2018, 139(1): 247-280.

DOI：10.1007/s00211-017-0932-4

We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations of different accuracy and computational work of the arguments of this map. We propose and analyze a generalized version of Smolyak's algorithm, which provides sparse approximation formulas with convergence rates that mitigate the curse of dimension that appears in multilinear approximation problems with a large number of arguments. We apply the general framework to response surface approximation and optimization under uncertainty for parametric partial differential equations using kernel-based approximation. The theoretical results are supplemented by numerical experiments.

• 出版日期2018-5
• 单位KAUST