Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, and then extend the construction to random field data via the Karhunen-Loeve expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model.

翻译：工程与应用科学依赖计算实验来严谨研究物理系统。用于探测这些系统的数学模型高度复杂，且采样密集的研究往往需要过多模拟才能获得可接受的精度。替代模型提供了一种规避此类复杂模型高计算成本采样问题的方法。具体而言，多项式混沌展开（PCE）已成功用于确定性模型的不确定性量化研究，其中不确定性的主要来源是参数性的。我们讨论了传统PCE替代建模的一种扩展方法，以支持在除参数不确定性外还存在内在噪声的随机计算模型的替代模型构建。通过Rosenblatt变换，我们在内在不确定性与参数不确定性的联合空间上开发了PCE替代模型，并进一步通过Karhunen-Loeve展开将其扩展至随机场数据。接着，我们利用计算PCE Sobol指标的闭式解对模型进行全局灵敏度分析，以量化内在噪声对整体模型输出方差的贡献。此外，生成的联合PCE具有生成性，即它能在任意输入参数设置下生成随机实现，且这些实现在统计上近似等价于底层随机模型的实现。该方法在化学催化示例模型上得到了验证。