Compressive sensing adaptation for polynomial chaos expansions

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.

Submitted to Journal of Computational Physics

References in corpus (4)

• Data-driven polynomial ridge approximation using variable projection
• Reduced Wiener Chaos representation of random fields via basis adaptation and projection
• Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations
• Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

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