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

本项目将基于差异和差异敏感性（DS）的数学定义，探索和开发一种新的方法，量化样本点对整个输入/输出域样本均匀性的贡献，以及由此产生的计算机实验设计策略（DoCE）。从本质上讲，DS量化了由于增加新的模拟样本点而导致的样本点均匀性的变化。该项目旨在推导“DS域”，以有效地定位新的样本点，制定DS策略，以最佳地选择下N个模拟点，并研究有效使用DS进行DoCE的一些开放问题。期望的结果是创新的算法，有效地选择响应面勘探的样本点，不确定性在复杂系统中的传播，以及设计优化。无论是模型验证、设计优化还是可靠性分析，在不确定性存在的情况下，很难有效地选择计算机实验的样本点。即使有了最近的计算进步，对复杂不确定系统的模拟仍然是当今最强大的计算机的负担。因此，需要在有限的计算预算下选择哪些模拟将提供最有用的信息的方法。这些问题在科学和工程中广泛存在，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，弹丸穿透，宇宙学模型和复杂系统可靠性方面的高优先级应用。存在一些选择样本点的方法，但缺乏对新样本点添加的“信息”的定量度量，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.