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.
@article{Tsilifis2018,
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}
}