实验设计：优化感兴趣的量以可靠地减少模型输入参数的不确定性
Experimental Design : Optimizing Quantities of Interest to Reliably Reduce the Uncertainty in Model Input Parameters
AI总结：
本文提出通过优化感兴趣的量来减少模型输入参数的不确定性，采用测度论框架解决正向和逆向问题，利用假设的QoI集量化几何特征，确定最优实验设计。
摘要：
随着利益相关者和政策制定者日益依赖高级计算模型的定量预测，一个根本性问题是量化和减少模型输入和输出数据的不确定性。端到端不确定性量化工作流程通常需要首先利用可用感兴趣的量（QoI）的输出数据来建立和求解随机逆问题（SIPs）。SIPs的解通常以模型输入空间上的概率测度或密度形式表示。然后可以建立和求解随机正向问题（SFP），将模型输入的不确定性传播通过模型，以对不可观测或未来的QoI数据做出定量预测。在本文中，我们使用测度论框架来建立和求解SIPs和SFPs。从这一角度来看，我们量化了使用假设的QoI集描述SIP和SFP解的精度和准确性的几何特征。这导致了最优实验设计的自然定义，即有限传感器集在时空中的最优配置。讨论了多个数值示例和应用，包括使用模拟数据从飓风Gustav确定墨西哥湾最佳浮标放置位置，以捕捉风暴潮的高水位，从而减少底粗糙度特征的不确定性。
英文摘要：
As stakeholders and policy makers increasingly rely upon quantitative predictions from advanced computational models, a problem of fundamental importance is the quantification and reduction of uncertainties in both model inputs and output data. The typical work-flow in the end-to-end quantification of uncertainties requires first formulating and solving stochastic inverse problems (SIPs) using output data on available quantities of interest (QoI). The solution to a SIP is often written in terms of a probability measure, or density, on the space of model inputs. Then, we can formulate and solve a stochastic forward problem (SFP) where the uncertainty on model inputs is propagated through the model to make quantitative predictions on either unobservable or future QoI data. In this work, we use a measure-theoretic framework to formulate and solve both SIPs and SFPs. From this perspective, we quantify the geometric characteristics of using hypothetical sets of QoI that describe both the precision and accuracy in solutions to both the SIP and SFP. This leads to a natural definition of the optimal experimental design, i.e., what the optimal configuration a finite set of sensors is in space-time. Several numerical examples and applications are discussed including the ADvanced CIRCulation (ADCIRC) model using simulated data from Hurricane Gustav to determine an optimal placement of buoys in the Gulf of Mexico to capture high water marks of the storm surge in order to reduce uncertainties in bottom roughness characteristics.
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