Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

摘要

Compressive-sensing-based uncertainty quantification methods have become apow- erful tool for problems with limited data. In this work, we use the slicedinverse regression (SIR) method to provide an initial guess for the alternatingdirection method, which is used to en- hance sparsity of the Hermite polynomialexpansion of stochastic quantity of interest. The sparsity improvementincreases both the efficiency and accuracy of the compressive-sensing- baseduncertainty quantification method. We demonstrate that the initial guess fromSIR is more suitable for cases when the available data are limited (Algorithm4). We also propose another algorithm (Algorithm 5) that performs dimensionreduction first with SIR. Then it constructs a Hermite polynomial expansion ofthe reduced model. This method affords the ability to approximate thestatistics accurately with even less available data. Both methods arenon-intrusive and require no a priori information of the sparsity of thesystem. The effec- tiveness of these two methods (Algorithms 4 and 5) aredemonstrated using problems with up to 500 random dimensions.