This paper proposes a general framework to estimate coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification via rotational sparse approximation. In particular, we aim to identify a rotation matrix such that the gPC expansion of a set of random variables after the rotation has a sparser representation. However, this rotational approach alters the underlying linear system to be solved, which makes finding the sparse coefficients more difficult than the case without rotation. To solve this problem, we examine several popular nonconvex regularizations in compressive sensing (CS) that perform better than the classic l1 approach empirically. All these regularizations can be minimized by the alternating direction method of multipliers (ADMM). Numerical examples show superior performance of the proposed combination of rotation and nonconvex sparse promoting regularizations over the ones without rotation and with rotation but using the convex l1 approach.

翻译：本文提出一个总框架,用于估计普遍多元混乱系数(gPC),用于通过轮换性稀疏近似度进行不确定性的量化,特别是,我们力求确定一个轮换矩阵,使GPC在轮换后扩大一组随机变数具有较稀小的代表性;然而,这种轮换方法改变了有待解决的基本线性系统,使得在不轮换的情况下找到稀疏系数比情况更困难。为了解决这个问题,我们研究了在压缩感中一些比经典的l1方法更好的非凝固规范化(CS),这些常规化可以通过乘数的交替方向方法(ADMM)加以最小化。数字实例显示,拟议将轮换和非凝固性混合起来,在不轮换和不轮换的情况下促进规范化,但采用矩形L1方法的优异性表现。