用于敏感性指数估计的认证元模型
Certified metamodels for sensitivity indices estimation
摘要：
数值代码的全局灵敏度分析，更具体地说，与输入变量相关联的Sobol指数的估计，通常需要大量的模型运行。当这些需要太多的计算时间时，有必要使用降阶模型（元模型）来执行灵敏度分析，其输出在数值上接近原始模型的输出，同时运行速度更快。在这种情况下，估计指数受到两种误差：抽样误差，所造成的计算积分出现在定义中的Sobol指数的蒙特卡罗方法，和元模型误差，所造成的替代原模型的元模型。在我们已经认证的元模型误差的界限的情况下，我们提出了一种方法来量化这两种类型的错误，我们计算置信区间的一阶Sobol指数。
英文摘要：
Global sensitivity analysis of a numerical code, more specifically estimation of Sobol indices associated with input variables, generally requires a large number of model runs. When those demand too much computation time, it is necessary to use a reduced model (metamodel) to perform sensitivity analysis, whose outputs are numerically close to the ones of the original model, while being much faster to run. In this case, estimated indices are subject to two kinds of errors: sampling error, caused by the computation of the integrals appearing in the definition of the Sobol indices by a Monte-Carlo method, and metamodel error, caused by the replacement of the original model by the metamodel. In cases where we have certified bounds for the metamodel error, we propose a method to quantify both types of error, and we compute confidence intervals for first-order Sobol indices.
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