Compressive sensing adaptation for polynomial chaos expansions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:380

Article

Tsilifis, Panagiotis^1,2  Huan, Xun^3,4  Safta, Cosmin⁴  Sargsyan, Khachik⁴  Lacaze, Guilhem⁴  Oefelein, Joseph C.⁴  Najm, Habib N.⁴  Ghanem, Roger G.² 

[1] Ecole Polytech Fed Lausanne, Inst Math, CSQI, CH-1015 Lausanne, Switzerland

[2] Univ Southern Calif, Sonny Astani Dept Civil Engn, Los Angeles, CA 90089 USA

[3] Univ Michigan, Dept Mech Engn, Ann Arbor, MI 48109 USA

[4] Sandia Natl Labs, 7011 East Ave, Livermore, CA 94550 USA

关键词: Polynomial chaos;    Basis adaptation;    Compressive sensing;    l(1)-Minimization;    Dimensionality reduction;    Uncertainty propagation;   

DOI  :  10.1016/j.jcp.2018.12.010

来源: Elsevier

【 摘 要 】

Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorithms, resulting in a reduced polynomial chaos approximation with optimal sparsity. The developed adaptation algorithm consists of a two-step optimization procedure that computes the optimal coefficients and the input projection matrix of a low dimensional chaos expansion with respect to an optimally rotated basis. We demonstrate the attractive features of our algorithm through several numerical examples including the application on Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE scramjet engine. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free