基于切片逆回归的旋转压缩感知方法用于不确定性量化
Sliced-Inverse-Regression-Aided Rotated Compressive Sensing Method for Uncertainty Quantification
AI总结：
本文提出基于切片逆回归的旋转压缩感知方法，用于提升随机量的赫尔米特多项式展开的稀疏性，提高不确定性量化的效率和准确性。
摘要：
基于压缩感知的不确定性量化方法已成为处理有限数据问题的强大工具。本文使用切片逆回归方法为交替方向法提供初始猜测，以增强随机量感兴趣量的赫尔米特多项式展开的稀疏性。稀疏性改进提高了基于压缩感知的不确定性量化方法的效率和准确性。我们证明了当可用数据有限时，来自SIR的初始猜测更合适（算法4）。我们还提出另一种算法（算法5），首先使用SIR进行降维，然后构建降维模型的赫尔米特多项式展开。该方法使即使在可用数据较少的情况下也能准确近似统计特性。这两种方法都是非侵入性的，不需要系统稀疏性的先验信息。这两种方法的有效性通过最多500个随机维度的问题得到验证。
英文摘要：
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.
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