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

本提案的主要目标是开发一个灵活的框架，用于大规模模拟的设计和建模，并广泛应用于其他统计领域。研究了一种多步拟合大量计算机模拟数据的方法，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精度和标称精度的理论界限。研究者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。大规模模拟广泛应用于科学和工程领域的复杂现象研究。以模拟代替物理实验以节省成本和时间的趋势近年来加速发展。拟议的研究从计算机模拟中获得动力，但广泛应用于其他统计领域，以模拟大量数据并从多个来源借用信息。除统计学外，该研究还将对离散数学、计算机科学和高性能计算做出重大贡献。通过期刊出版物、工业合作和开源软件的发布进行传播，将导致广泛采用已开发的研究，从而显著改善美国工业中复杂模拟的使用。该研究将对国家实验室严格的不确定性量化工作具有相当大的附加价值，以支持国家安全。培训来自代表性不足群体的学生将通过基于谜题的学习方法来完成。研究生将受益于统计学和优化之间的接口的多学科训练。博士生将遵循平衡统计理论和实践的威斯康星模式进行监督，并获得第一手的研究经验，他们可以为自己的职业生涯借鉴。

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.