Multifidelity (MF) uncertainty quantification (UQ) seeks to leverage and fuse information from a collection of models to achieve greater statistical accuracy with respect to a single-fidelity counterpart, while maintaining an efficient use of computational resources. Despite many recent advancements in MF UQ, several challenges remain and these often limit its practical impact in certain application areas. In this manuscript, we focus on the challenges introduced by nondeterministic models to sampling MF UQ estimators. Nondeterministic models produce different responses for the same inputs, which means their outputs are effectively noisy. MF UQ is complicated by this noise since many state-of-the-art approaches rely on statistics, e.g., the correlation among models, to optimally fuse information and allocate computational resources. We demonstrate how the statistics of the quantities of interest, which impact the design, effectiveness, and use of existing MF UQ techniques, change as functions of the noise. With this in hand, we extend the unifying approximate control variate framework to account for nondeterminism, providing for the first time a rigorous means of comparing the effect of nondeterminism on different multifidelity estimators and analyzing their performance with respect to one another. Numerical examples are presented throughout the manuscript to illustrate and discuss the consequences of the presented theoretical results.

中文翻译：

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开发基于样本的非确定性模型多精度估计器的挑战分析

多重保真度 (MF) 不确定性量化 (UQ) 旨在利用和融合模型集合中的信息，以实现相对于单保真度对应物更高的统计准确性，同时保持计算资源的有效利用。尽管 MF UQ 最近取得了许多进展，但仍然存在一些挑战，这些挑战往往限制了其在某些应用领域的实际影响。在这篇手稿中，我们重点关注非确定性模型给 MF UQ 估计采样带来的挑战。不确定性模型对相同的输入产生不同的响应，这意味着它们的输出实际上是有噪声的。 MF UQ 因这种噪声而变得复杂，因为许多最先进的方法依赖于统计数据（例如模型之间的相关性）来最佳地融合信息并分配计算资源。我们演示了影响现有 MF UQ 技术的设计、有效性和使用的感兴趣数量的统计数据如何随着噪声的函数而变化。有了这个，我们扩展了统一的近似控制变量框架来解释非确定性，第一次提供了一种严格的方法来比较非确定性对不同多保真度估计器的影响并分析它们相对于彼此的性能。整个手稿中都提供了数值示例，以说明和讨论所提出的理论结果的后果。