PNNL

Abstract

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this paper, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic state variables. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for the cases when the available data is very limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with sliced inverse regression, then constructs a Hermite polynomial expansion of the reduced model. This method allows us to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. We demonstrate the effectiveness of these two methods (Algorithms 4 and 5) using problems with up to 500 random dimensions.