Sliced-Inverse-Regression-Aided Rotated Compressive Sensing Method for Uncertainty Quantification
This work addresses the challenge of uncertainty quantification in high-dimensional systems with scarce data, offering non-intrusive methods that require no prior sparsity information.
The paper proposes two algorithms that integrate sliced inverse regression with compressive sensing to improve uncertainty quantification for high-dimensional stochastic problems with limited data, demonstrating effectiveness on problems with up to 500 random dimensions.
Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this work, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to en- hance sparsity of the Hermite polynomial expansion of stochastic quantity of interest. 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 cases when the available data are limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with SIR. Then it constructs a Hermite polynomial expansion of the reduced model. This method affords the ability 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. The effec- tiveness of these two methods (Algorithms 4 and 5) are demonstrated using problems with up to 500 random dimensions.