Compressive sensing adaptation for polynomial chaos expansion


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.

P. Tsilifis, X. Huan, C. Safta, K. Sargsyan, G. Lacaze, J. C. Oefelein, Habib N. Najm, and R. G. Ghanem. Compressive sensing adaptation for polynomial chaos expansions. arXiv preprint, arXiv:1801.01961, 2018.


author = {Tsilifis, Panagiotis and Huan, Xun and Safta, Cosmin and Sargsyan, Khachik and Lacaze, Guilhem and Oefelein, Joseph C. and Najm, Habib N. and Ghanem, Roger G.},
journal = {arXiv preprint arXiv:1801.01961},
title = {{Compressive sensing adaptation for polynomial chaos expansions}},
year = {2018}