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

NSF/桑迪亚：在设计和不确定性量化中有效选择计算机实验的差异敏感性

• 批准号: 0331145
• 负责人: Erik Johnson
• 金额: --
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0331145&HistoricalAwards=false
• 关键词: NSF; Sandia; Discrepancy; Sensitivity; Efficiently

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.

该项目将探索和开发一种新方法，基于差异和差异敏感性（DS）的数学定义，量化样本点对整个输入/输出域中样本均匀性的贡献，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。 该项目的目标是导出“DS 字段”以有效地定位新的样本点，制定 DS 策略以最好地选择接下来的 N 个模拟点，并研究有效使用 DS 进行 DoCE 所必需的一些开放性问题。 预期的结果是为响应面探索、不确定性通过复杂系统的传播和设计优化有效选择样本点的创新算法。无论是模型验证、设计优化还是可靠性分析，在存在不确定性的情况下，很难有效地选择计算机实验的样本点。 即使最近的计算技术取得了进步，复杂的不确定系统的模拟仍然对当今最强大的计算机造成负担。 因此，需要一些方法来选择哪些模拟将在给定有限的计算预算的情况下提供最有用的信息。 此类问题在科学和工程中普遍存在，由于财务、安全、政策或其他务实原因，物理测试通常不切实际，并且包括事故调查、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。 存在一些选择样本点的方法，但缺乏对新样本点添加的“信息”的定量测量，特别是在输出空间中。