CAREER: A flexible design and modeling framework for computer experiments and beyond

职业：用于计算机实验及其他领域的灵活设计和建模框架

• 批准号: 1055214
• 负责人: Peter Chien
• 金额: $ 40万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-06-01 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1055214&HistoricalAwards=false
• 关键词: CAREER; flexible; design; modeling; framework

The primary objective of this proposal is to develop a flexible framework for design and modeling of large-scale simulations with broad applications to other areas of statistics. The investigator studies a multi-step method for fitting massive data from computer simulations that can simultaneously mitigate singularity and improve accuracy of interpolation. Theoretical bounds on numeric and nominal accuracy of this method will be derived. The investigator also proposes new designs inspired by Sudoku to efficiently pool data from multiple sources and employs sliced Latin hypercube designs to enhance stochastic optimization and cross-validation.Large-scale simulations are widely used for studying complex phenomena in sciences and engineering. The trend of replacing physical experiments with simulations to save cost and time has accelerated recently. The proposed research draws impetus from computer simulations but applies broadly to other areas of statistics for modeling massive data and for borrowing information from multiple sources. Beyond statistics, the research will make significant contributions to discrete mathematics, computer science and high-performance computing. Dissemination through journal publications, industrial collaborations and release of open source software will result in broad adoption of the developed research to significantly improve the use of complex simulations in U.S. industries. The research will be of considerable added value to rigorous uncertainty quantification efforts by national laboratories to support national security. Training students from under-represented groups will be accomplished through a puzzle based learning approach. Graduate students will benefit through multidisciplinary training on the interface between statistics and optimization. Ph.D. students will be supervised by following the Wisconsin model of balancing statistical theory and practice, and obtain first-hand research experience they can draw on for their careers.

该提案的主要目标是开发一个灵活的框架，用于设计和建模的大规模模拟与广泛的应用，以其他领域的统计。研究人员研究了一种多步方法，用于从计算机模拟中拟合大量数据，该方法可以同时减轻奇异性并提高插值精度。将推导出该方法的数值和标称精度的理论界限。研究人员还提出了受数独启发的新设计，以有效地汇集来自多个来源的数据，并采用切片拉丁超立方体设计来增强随机优化和交叉验证。大规模模拟广泛用于研究科学和工程中的复杂现象。为了节省成本和时间，用模拟代替物理实验的趋势最近有所加快。拟议的研究从计算机模拟中汲取动力，但广泛适用于其他统计领域，用于建模海量数据和从多个来源借用信息。除了统计学，这项研究还将为离散数学、计算机科学和高性能计算做出重大贡献。通过期刊出版物、行业合作和开源软件的发布进行传播，将导致开发的研究得到广泛采用，从而显著改善美国行业复杂模拟的使用。这项研究将对国家实验室为支持国家安全而进行的严格的不确定性量化工作具有相当大的附加值。来自代表性不足群体的学生的培训将通过基于谜题的学习方法来完成。研究生将通过统计和优化之间的接口多学科培训受益。博士学生将遵循平衡统计理论和实践的威斯康星州模式进行监督，并获得第一手的研究经验，他们可以借鉴他们的职业生涯。