Compressive sensing adaptation for polynomial chaos expansions

TL;DR

This paper introduces a novel basis adaptation method for polynomial chaos expansions using compressive sensing, achieving sparse, efficient representations and demonstrating effectiveness in turbulent combustion simulations.

Contribution

It presents a new two-step optimization algorithm combining compressive sensing with basis rotation for improved polynomial chaos approximation.

Findings

Achieves sparse polynomial chaos representations with fewer basis functions.

Demonstrates effectiveness in complex turbulent combustion simulations.

Provides a flexible adaptation mechanism with good convergence properties.

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.