Metamodeling of complex numerical systems has recently attracted the interest of the mathematical programming community. Despite the progress in high performance computing, simulations remain costly, as a matter of fact, the assessment of the exposure to radio frequency electromagnetic fields is computationally prohibitive since one simulation can require hours. Moreover, in many engineering problems, carrying out deterministic numerical operations without considering uncertainties can lead to unreliable designs. In this paper we focus on the surrogate modeling of a particular type of computational models called stochastic simulators. In contrast to deterministic simulators which yield a unique output for each set of input parameters, stochastic simulators inherently contain some sources of randomness and the output at a given point is a probability density function. Characterizing the stochastic simulators is even more time consuming. This paper represents stochastic simulators as a stochastic process and describes a metamodeling approach based on the Karhunen-Loeve spectral decomposition.

中文翻译：

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随机函数的替代建模 - 在计算电磁剂量学中的应用

复杂数值系统的元建模最近引起了数学编程社区的兴趣。尽管在高性能计算方面取得了进展，但模拟仍然成本高昂，事实上，对射频电磁场暴露的评估在计算上是令人望而却步的，因为一次模拟可能需要数小时。此外，在许多工程问题中，在不考虑不确定性的情况下执行确定性数值运算会导致设计不可靠。在本文中，我们专注于称为随机模拟器的特定类型计算模型的代理建模。与为每组输入参数产生唯一输出的确定性模拟器相比，随机模拟器固有地包含一些随机源，并且给定点的输出是概率密度函数。表征随机模拟器甚至更耗时。本文将随机模拟器表示为一个随机过程，并描述了一种基于 Karhunen-Loeve 谱分解的元建模方法。