Due to limited computational power, performing uncertainty quantification analyses with complex computational models can be a challenging task. This is exacerbated in the context of stochastic simulators, the response of which to a given set of input parameters, rather than being a deterministic value, is a random variable with unknown probability density function (PDF). Of interest in this paper is the construction of a surrogate that can accurately predict this response PDF for any input parameters. We suggest using a flexible distribution family -- the generalized lambda distribution -- to approximate the response PDF. The associated distribution parameters are cast as functions of input parameters and represented by sparse polynomial chaos expansions. To build such a surrogate model, we propose an approach based on a local inference of the response PDF at each point of the experimental design based on replicated model evaluations. Two versions of this framework are proposed and compared on analytical examples and case studies.

中文翻译：

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使用广义 lambda 分布对随机模拟器的响应分布进行基于复制的仿真

由于计算能力有限，使用复杂的计算模型进行不确定性量化分析可能是一项具有挑战性的任务。这在随机模拟器的背景下更加严重，其对给定输入参数集的响应，而不是确定性值，是具有未知概率密度函数 (PDF) 的随机变量。本文感兴趣的是构建一个可以准确预测任何输入参数的响应 PDF 的代理。我们建议使用灵活的分布族——广义 lambda 分布——来近似响应 PDF。相关的分布参数被转换为输入参数的函数，并由稀疏多项式混沌展开式表示。为了建立这样的代理模型，我们提出了一种基于重复模型评估的实验设计每个点响应 PDF 的局部推断的方法。提出了该框架的两个版本，并在分析示例和案例研究中进行了比较。