NSF/Sandia: Discrepancy Sensitivity for Efficiently Choosing Computer Experiments in Design and Uncertainty Quantification

本项目将探索和开发一种新的方法，基于差异和差异灵敏度（DS）的数学定义，在整个输入/输出域中量化样本点对样本均匀性的贡献，以及由此产生的计算机实验设计策略（DoCE）。本质上，DS量化了由于添加新的模拟样本点而导致的样本点均匀性的变化。 该项目的目标是获得“DS字段”，以有效地定位一个新的样本点，开发DS策略，以最好地选择接下来的N个模拟点，并调查一些开放的问题，以有效地使用DS的DoCE。 期望的结果是有效地选择响应面探索，通过复杂系统的不确定性传播，和设计优化的样本点的创新算法。无论是模型验证，设计优化或可靠性分析，它是很难有效地选择样本点的计算机实验中存在的不确定性。 即使最近的计算进步，复杂的不确定系统的模拟税收今天最有能力的计算机。 因此，需要方法来选择哪些模拟将提供最有用的信息，给定有限的计算预算。 这样的问题在科学和工程中是普遍存在的，其中物理测试通常出于财务、安全、政策或其他实用原因而不切实际，并且包括在事故调查、蛋白质建模、射弹穿透、宇宙学模型和复杂系统可靠性中的高优先级应用。 存在一些用于选择样本点的方法，但是缺乏对由新样本点添加的“信息”的定量测量，特别是在输出空间中。

This project will explore and develop a new method, based on the mathematical definitions of discrepancy and discrepancy sensitivity (DS), of quantifying sample point contribution to sample uniformity in the entire input/output domain, and the resulting strategies for the design of computer experiments (DoCE). Essentially, DS quantifies the change in sample point uniformity due to the addition of new simulation sample points. The project will aim to derive "DS fields" to efficiently locate a new sample point, develop DS strategies to best choose the next N simulation points, and investigate a number of open questions integral to effective use of DS for DoCE. The expected results are innovative algorithms for efficiently choosing sample points for response surface exploration, propagation of uncertainty through complex systems, and design optimization.Whether for model validation, design optimization or reliability analysis, it is difficult to efficiently choose sample points for computer experiments in the presence of uncertainty. Even with recent computational advances, simulation of complex uncertain systems taxes today's most capable computers. Thus, methods are required to select which simulations will provide the most useful information given a limited computational budget. Such problems are widespread in science and engineering, where physical testing is often impractical for financial, safety, policy or other pragmatic reasons, and include high-priority applications in accident investigation, protein modeling, projectile penetration, cosmological models, and complex system reliability. Some approaches exist for choosing sample points, but lack quantitative measures of "information" added by new sample points, particularly in the output space.