A weighted l1-minimization approach for sparse polynomial chaos expansions
A weighted l1-minimization approach for sparse polynomial chaos expansions
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DOI：
10.1016/j.jcp.2014.02.024
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
Jigen Peng;Jerrad Hampton;A. Doostan
中科院分区：
文献类型：
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作者：
Jigen Peng;Jerrad Hampton;A. Doostan
提出了一种基于非自适应随机采样的高维随机函数稀疏多项式混沌逼近方法。我们修改标准的最小化算法，最初提出的压缩采样的背景下，使用先验信息的PC系数的衰减，当可用时，并将得到的算法作为加权最小化。我们提供的条件下，我们可以保证恢复使用这种加权方案。数值试验被用来比较的加权和非加权的方法恢复的解决方案，两个高维随机输入的微分方程：随机椭圆算子的边值问题和二维热驱动空腔流的随机边界条件。
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard ℓ 1-minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients, when available, and refer to the resulting algorithm as weighted ℓ 1-minimization. We provide conditions under which we may guarantee recovery using this weighted scheme. Numerical tests are used to compare the weighted and non-weighted methods for the recovery of solutions to two differential equations with high-dimensional random inputs: a boundary value problem with a random elliptic operator and a 2-D thermally driven cavity flow with random boundary condition.