Quasi-Monte Carlo and RBF Metamodeling for Quantile Estimation in River Bed Morphodynamics
Quasi-Monte Carlo and RBF Metamodeling for Quantile Estimation in River Bed Morphodynamics
复制标题
用于河床形态动力学分位数估计的准蒙特卡罗和 RBF 元建模
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Pott
中科院分区：
文献类型：
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作者：
T. Clees;I. Nikitin;L. Nikitina;S. Pott
比较了四种常用的分位数估计方法：蒙特卡罗（MC）、Harrel-Davis加权蒙特卡罗（WMC）、Sobol序列拟蒙特卡罗（QMC）和拟随机样条（QRS）。该方法与RBF元模型相结合，并应用于河床演变的形态动力学-水动力学模拟分析。取得了以下结果。Harrel-Davis加权在少量样本N ~ 100时可使精度适度提高10- 20%。准蒙特卡罗方法显著提高了分位数精度，例如，实现rms ~ 10−4精度所需的函数计算数量从MC的1，000，000减少到QMC的100，000和QRS的6，000。另一方面，大数据的RBF元建模可以加快计算一个完整的结果在所考虑的问题从45分钟（32 CPU）到20秒（1 CPU），提供快速的分位数估计整个庞大的数据集。
Four generic methods for quantile estimation have been compared: Monte Carlo (MC), Monte Carlo with Harrel-Davis weighting (WMC), quasi-Monte Carlo with Sobol sequence (QMC) and quasi-random splines (QRS). The methods are combined with RBF metamodel and applied to the analysis of morphodynamic—hydrodynamic simulations of the river bed evolution. The following results have been obtained. Harrel-Davis weighting gives a moderate 10–20 % improvement of precision at small number of samples N ~ 100. Quasi-Monte Carlo methods provide significant improvement of quantile precision, e.g. the number of function evaluations necessary to achieve rms ~ 10−4 precision is reduced from 1,000,000 for MC to 100,000 for QMC and to 6,000 for QRS. On the other hand, RBF metamodeling of bulky data allows to speed up the computation of one complete result in the considered problem from 45 min (on 32CPU) to 20 s (on 1CPU), providing rapid quantile estimation for the whole set of bulky data.