Compressive sensing adaptation for polynomial chaos expansions
This work addresses the need for more efficient uncertainty quantification in computational models, such as turbulent combustion, but appears incremental as it builds on existing compressive sensing and basis adaptation methods.
The paper tackles the problem of improving polynomial chaos expansions by introducing a new adaptation mechanism based on compressive sensing, resulting in a reduced approximation with optimal sparsity, as demonstrated through numerical examples including turbulent combustion simulations.
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.