Analytic regularity and stochastic collocation of high-dimensional Newton iterates
Analytic regularity and stochastic collocation of high-dimensional Newton iterates
复制标题
高维牛顿迭代的解析正则性与随机配置
DOI：
10.1007/s10444-020-09791-1
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发表时间：
2020
影响因子：
1.7
通讯作者：
Kon, Mark
中科院分区：
文献类型：
--
作者：
Castrillón-Candás, Julio E.;Kon, Mark
在本文中，我们介绍的概念，从不确定性量化（UQ）和数值分析的有效评估随机高维牛顿迭代。特别是，我们开发了复杂的解析正则性理论的解决方案，就随机变量。这证明了稀疏网格的应用程序的统计措施的计算。收敛速度的推导和证明是次指数或代数的随机扰动的实现的数量。由于该方法的准确性，稀疏网格非常适合计算具有高置信度的低概率事件。我们将我们的方法应用到潮流问题。在具有大随机负荷的非平凡新英格兰39节点电力系统模型上进行的数值实验与理论收敛速度一致。与Monte Carlo方法相比，在相同精度下，该方法的计算速度至少提高了1011倍.
In this paper, we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high-dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the solution with respect to the random variables. This justifies the application of sparse grids for the computation of statistical measures. Convergence rates are derived and are shown to be subexponential or algebraic with respect to the number of realizations of random perturbations. Due to the accuracy of the method, sparse grids are well suited for computing low-probability events with high confidence. We apply our method to the power flow problem. Numerical experiments on the non-trivial, 39-bus New England power system model with large stochastic loads are consistent with the theoretical convergence rates. Moreover, compared with the Monte Carlo method, our approach is at least 1011times faster for the same accuracy.
DOI：
10.1007/978-94-009-0491-0_5
发表时间：
1965
期刊：
Science China Mathematics
影响因子：
--
作者：
N. Bogolubov;A. Logunov;A. Oksak;I. Todorov;G. Gould
通讯作者：
G. Gould
影响因子：
6.6
作者：
Zimmerman, Ray Daniel;Edmundo Murillo-Sanchez, Carlos;Thomas, Robert John
通讯作者：
Thomas, Robert John