Stochastic simulators are non-deterministic computer models which provide a different response each time they are run, even when the input parameters are held at fixed values. They arise when additional sources of uncertainty are affecting the computer model, which are not explicitly modeled as input parameters. The uncertainty analysis of stochastic simulators requires their repeated evaluation for different values of the input variables, as well as for different realizations of the underlying latent stochasticity. The computational cost of such analyses can be considerable, which motivates the construction of surrogate models that can approximate the original model and its stochastic response, but can be evaluated at much lower cost. We propose a surrogate model for stochastic simulators based on spectral expansions. Considering a certain class of stochastic simulators that can be repeatedly evaluated for the same underlying random event, we view the simulator as a random field indexed by the input parameter space. For a fixed realization of the latent stochasticity, the response of the simulator is a deterministic function, called trajectory. Based on samples from several such trajectories, we approximate the latter by sparse polynomial chaos expansion and compute analytically an extended Karhunen-Lo\`eve expansion (KLE) to reduce its dimensionality. The uncorrelated but dependent random variables of the KLE are modeled by advanced statistical techniques such as parametric inference, vine copula modeling, and kernel density estimation. The resulting surrogate model approximates the marginals and the covariance function, and allows to obtain new realizations at low computational cost. We observe that in our numerical examples, the first mode of the KLE is by far the most important, and investigate this phenomenon and its implications.
翻译:视觉模拟器的不确定性分析要求反复评估输入变量的不同值,以及潜在潜在随机性的不同认识。这种分析的计算成本可能相当可观,这种分析的计算成本可以鼓励构建替代模型,这些模型可以接近原始模型及其随机反应,但可以以低得多的成本进行评估。当更多的不确定性源影响计算机模型时,这些不确定性源并不明显作为输入参数模型模型。对随机模拟器的不确定性分析要求反复评估输入变量的不同值,以及对于潜在潜在潜在随机性的不同认识。这种分析的计算成本可以相当可观,这种模型的计算成本可以鼓励构建替代模型,这些模型可以接近原始模型及其随机分析反应,但可以以低得多的成本评估。我们建议基于光谱扩展的随机模拟器的替代模型模型模型模型模型模型模型模型。我们通过输入空间的随机模型模型将这个模拟模型作为随机模型的模型,对于潜伏性模型的预测值而言,其随机值的预测值反应,但以低成本值为低得多的成本评估,我们建议基于光谱化的统计变量的模型,因此,在远端分析轨道上进行。