SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 3, Page 860-890, January 2020.
In this paper, we address uncertainty quantification of physics-based computational models when the quantity of interest concerns geometrical characteristics of their spatial response. Within the probabilistic context of the random set theory, we develop the concept of confidence sets that either contain or are contained within an excursion set of the spatial response with a specified probability level. We seek such confidence sets in a parametric family of nested candidate sets defined as a parametric family of sublevel or superlevel sets of a membership function. We show that the problem of identifying a confidence set with a given probability level in such a parametric family is equivalent to a problem of estimating a quantile of a random variable obtained as a global extremum of the membership function over the complement of the excursion set. To construct such confidence sets, we propose a computationally efficient bifidelity method that exploits a spectral representation of this random variable to reduce the required number of evaluations of the computational model. We show the interest of this concept of confidence sets and the efficiency gain of the proposed bifidelity method in an illustration relevant to the retreat of the grounded portion of the Antarctic ice sheet.

中文翻译：

---

基于多保真分位数的随机偏移集置信集方法及其在冰床动力学中的应用

SIAM / ASA不确定性量化期刊，第8卷，第3期，第860-890页，2020年1月。
在本文中，当感兴趣的数量涉及其空间响应的几何特征时，我们将解决基于物理的计算模型的不确定性量化问题。在随机集理论的概率背景下，我们发展了置信集的概念，该置信集包含或包含在具有指定概率水平的空间响应偏移集中。我们在嵌套候选集的参数族中寻求这样的置信集，该候选集定义为隶属函数的子级或超级集的参数族。我们表明，在这样一个参数族中识别具有给定概率水平的置信度集的问题等同于估算作为偏移集补集上的隶属函数的全局极值而获得的随机变量的分位数的问题。为了构造这种置信度集，我们提出了一种计算有效的双保真度方法，该方法利用此随机变量的频谱表示来减少计算模型评估所需的次数。我们在与南极冰盖接地部分的撤退有关的插图中显示了置信集概念的有效性和所提出的双保真方法的效率增益。