Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion. We use alternating direction method to identify new sets of random variables through iterative rotations such that the new representation of the uncertainty is sparser. Consequently, we increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. We demonstrate that the previously developed iterative method to enhance the sparsity of Hermite polynomial expansion is a special case of this general framework. Moreover, we use Legendre and Chebyshev polynomials expansions to demonstrate the effectiveness of this method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.

中文翻译：

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增强广义多项式混沌扩展稀疏性的通用框架

当只有有限的数据可用时，压缩感知已成为不确定性量化的有力补充。在本文中，我们提供了一个通用框架，以广义多项式混沌扩展的形式增强不确定性表示的稀疏性。我们使用交替方向方法通过迭代旋转来识别新的随机变量集，从而使不确定性的新表示更加稀疏。因此，我们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。我们证明了先前开发的用于增强 Hermite 多项式展开稀疏性的迭代方法是这个通用框架的一个特例。而且，