随机模拟码的模拟器
Emulators for stochastic simulation codes
摘要：
数值模拟代码是研究复杂现象的常用工具，但它们通常很耗时并且被认为是黑箱。对于某些统计研究（例如资产管理、灵敏度分析）或最优化问题（例如分子模型的调整），需要运行这种代码的高游程数。因此，基于实验设计构建此代码的快速运行近似（或元模型）更为方便。本文的主题是随机码的元模型的定义。与确定性代码相反，当使用相同的输入多次调用随机代码时，它们会给出不同的结果。在本文中，提出了两种方法来建立一个随机码输出的密度函数的元模型。第一个是基于核回归和第二个包括在分解的基础上精心选择的密度函数的输出密度，与连接的系数和输入参数的元模型。对于第二种方法，提出了两种类型的分解，但尚未为系数设计元模型。这是未来研究的一个课题。这些方法被应用到两个分析模型和三个工业案例。
英文摘要：
Numerical simulation codes are very common tools to study complex phenomena, but they are often time-consuming and considered as black boxes. For some statistical studies (e.g. asset management, sensitivity analysis) or optimization problems (e.g. tuning of a molecular model), a high number of runs of such codes is needed. Therefore it is more convenient to build a fast-running approximation - or metamodel - of this code based on a design of experiments. The topic of this paper is the definition of metamodels for stochastic codes. Contrary to deterministic codes, stochastic codes can give different results when they are called several times with the same input. In this paper, two approaches are proposed to build a metamodel of the probability density function of a stochastic code output. The first one is based on kernel regression and the second one consists in decomposing the output density on a basis of well-chosen probability density functions, with a metamodel linking the coefficients and the input parameters. For the second approach, two types of decomposition are proposed, but no metamodel has been designed for the coefficients yet. This is a topic of future research. These methods are applied to two analytical models and three industrial cases.
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