Compressive sensing adaptation for polynomial chaos expansions

Panagiotis Tsilifis; Xun Huan; Cosmin Safta; Khachik Sargsyan; Guilhem Lacaze; Joseph C. Oefelein; Habib N. Najm; Roger G. Ghanem

doi:10.1016/j.jcp.2018.12.010

arXiv · 1801.01961

Compressive sensing adaptation for polynomial chaos expansions

Panagiotis Tsilifis·Xun Huan·Cosmin Safta·Khachik Sargsyan·Guilhem Lacaze·Joseph C. Oefelein·Habib N. Najm·Roger G. Ghanem

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Abstract

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.

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Panagiotis Tsilifis, Xun Huan, Cosmin Safta, Khachik Sargsyan, Guilhem Lacaze, Joseph C. Oefelein, Habib N. Najm, Roger G. Ghanem. 2018-01-06. Compressive sensing adaptation for polynomial chaos expansions. https://doi.org/10.1016/j.jcp.2018.12.010

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