标题： 关于模型失配的超微分灵敏度分析：先验分布 显示英文标题

标题： Hyper-differential sensitivity analysis with respect to model discrepancy: Prior Distributions

摘要： 针对模型差异的超微分灵敏度分析最近被开发出来，以实现优化问题的不确定性量化。 该方法包括两个主要步骤：（i）高保真和低保真模型之间差异的贝叶斯校准，以及（ii）通过优化问题传播模型差异的不确定性。 当高保真模型评估受到限制时，如实践中常见的情况，先验差异分布在不确定性分析中起着至关重要的作用。 然而，由于其数学复杂性和许多超参数，指定这个先验具有挑战性。 本文提出了一种指定先验分布的新方法。 我们的方法分为两部分：（1）一种算法初始化先验超参数的方法，使用现有数据来初始化超参数估计值；（2）一个可视化框架，系统地探索先验的特性，并指导超参数的调整，以确保先验捕获适当的不确定性范围。 我们提供了详细的数学分析和一组数值例子，阐明了确保不确定性量化的关键先验特性。 显示英文摘要

摘要： Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the discrepancy between high- and low-fidelity models, and (ii) propagating the model discrepancy uncertainty through the optimization problem. When high-fidelity model evaluations are limited, as is common in practice, the prior discrepancy distribution plays a crucial role in the uncertainty analysis. However, specification of this prior is challenging due to its mathematical complexity and many hyper-parameters. This article presents a novel approach to specify the prior distribution. Our approach consists of two parts: (1) an algorithmic initialization of the prior hyper-parameters that uses existing data to initialize a hyper-parameter estimate, and (2) a visualization framework to systematically explore properties of the prior and guide tuning of the hyper-parameters to ensure that the prior captures the appropriate range of uncertainty. We provide detailed mathematical analysis and a collection of numerical examples that elucidate properties of the prior that are crucial to ensure uncertainty quantification.