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：工程学与应用科学依赖计算实验来严格研究物理系统。用于探究这些系统的数学模型高度复杂，而采样密集型研究通常需要大量模拟才能达到可接受的精度，这往往难以实现。代理模型提供了一种规避此类复杂模型高计算成本的途径。特别是，多项式混沌展开（PCEs）已成功应用于确定性模型的不确定性量化研究，其中参数不确定性是主要来源。本文讨论了传统PCE代理建模的扩展，旨在为除了参数不确定性外还具有固有噪声的随机计算模型构建代理。我们通过在固有不确定性和参数不确定性的联合空间上构建PCE代理模型（借助Rosenblatt变换实现），进而通过Karhunen-Loeve展开将构建方法扩展到随机场数据。随后，我们利用计算PCE Sobol指数的闭式解对模型进行全局敏感性分析，量化了固有噪声对模型总输出方差的贡献。此外，所得的联合PCE具有生成特性，即它允许在任何输入参数设置下生成随机实现，这些实现与底层随机模型的实现具有统计近似等价性。该方法在一个化学催化示例模型上得到了验证。