Sparse polynomial chaos expansion based on Bregman-iterative greedy coordinate descent for global sensitivity analysis

Abstract

Polynomial chaos expansion (PCE) is widely used in a variety of engineering fields for uncertainty and sensitivity analyses. The computational cost of full PCE is unaffordable due to the ‘curse of dimensionality’ of the expansion coefficients. In this paper, a novel methodology for developing sparse PCE is proposed by making use of the efficiency of greedy coordinate descent (GCD) in sparsity exploitation and the capability of Bregman iteration in accuracy enhancement. By minimizing an objective function composed of the l1 norm (sparsity) of the polynomial chaos (PC) coefficients and regularized l2 norm of the approximation fitness, the proposed algorithm screens the significant basis polynomials and builds an optimal sparse PCE with model evaluations much fewer than unknown coefficients. To validate the effectiveness of the developed algorithm, several benchmark examples are investigated for global sensitivity analysis (GSA). A detailed comparison is made with the well-established orthogonal matching pursuit (OMP), least angle regression (LAR) and two adaptive algorithms. Results show that the proposed method is superior to the benchmark methods in terms of accuracy while maintaining a better balance among accuracy, complexity and computational efficiency.