Collaborative Research: Uncertainty Quantification, Optimal Designs and Calibration in Computer Experiments

协作研究：计算机实验中的不确定性量化、优化设计和校准

• 批准号: 1914632
• 负责人: C. F. Jeff Wu
• 金额: $ 18万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1914632&HistoricalAwards=false
• 关键词: Collaborative; Research; Uncertainty; Quantification; Optimal

From aerospace designs to material science to biomedical studies, today's practice in engineering and physical sciences has made increasing use of computer simulations. How to design the computer simulations, analyze the computer output data, as well as to enhance the accuracy of the computer models are fundamental challenges in computer simulations. This project will focus on the development of a statistical framework for computer experiments, with the goal of developing both theoretical and methodological tools that cover the typical computer simulation pipeline from data collection to modeling and analysis to verification and validation. Specifically, the team plans to establish a new uncertainty quantification theory and foster novel methodologies for data mining, interpretation and decision making. The project will provide accurate, efficient and robust approaches that would make an impact on contemporary computer simulation practice. A graduate student will work on both the theoretical derivations and numerical verification for the project.The project has three major objectives: (i) establish a statistically and computationally efficient uncertainty quantification framework for Gaussian process regression, (ii) propose a general experimental design scheme for multi-fidelity computer experiments, (iii) study the statistical properties and suggest efficient algorithms for novel calibration methods for computer models. The proposed work should lead to methodological development of a generic nature in the design, uncertainty quantification and calibration in computer experiments. The improved uniform error bounds can potentially lead to the use of fewer experimental runs for the same precision. Their significance can go beyond computer experiments such as in spatial statistics, which heavily uses kriging method. The optimal designs for nonstationary Gaussian Process models can help stimulate further development of experimental design theory in more complex situations. Standard approaches in experimental design do not pay much attention to the nonstationary situations. The proposed algorithm can substantially enhance the value of the projected kernel calibration (PKC) method. Although PKC is known to be theoretically superior, there is no known algorithm that can effectively calculate the PKC estimates. Because calibration is used to bridge the gap between computer simulations and physical experiments, this work can be potentially significant. Theoretical and technical advances made in this project can help facilitate further interactions between statistics, applied mathematics and probability theory, through journal publications, student exchange visits and presentations in interdisciplinary conferences, etc.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

从航空航天设计到材料科学再到生物医学研究，今天的工程和物理科学实践越来越多地使用计算机模拟。如何设计计算机仿真，分析计算机输出数据，以及提高计算机模型的精度，是计算机仿真的根本挑战。该项目将侧重于开发计算机实验的统计框架，目标是开发理论和方法工具，涵盖从数据收集到建模和分析再到验证和验证的典型计算机模拟流程。具体地说，该团队计划建立一种新的不确定性量化理论，并培育用于数据挖掘、解释和决策的新方法。该项目将提供准确、高效和可靠的方法，对当代计算机模拟实践产生影响。该项目有三个主要目标：(I)为高斯过程回归建立一个统计上和计算上都有效的不确定性量化框架；(Ii)提出一个多保真计算机实验的通用实验设计方案；(Iii)研究计算机模型的统计特性，并为新的校准方法提出有效的算法。拟议的工作应导致在设计、计算机实验的不确定度量化和校准中发展具有一般性的方法学。改进的统一误差界可能会导致在相同精度下使用更少的实验运行。它们的意义可以超越计算机实验，例如在大量使用克里格法的空间统计学中。非平稳高斯过程模型的优化设计有助于在更复杂的情况下促进实验设计理论的进一步发展。实验设计中的标准方法不太注意非平稳情况。该算法大大提高了投影核校准(PKC)方法的性能。虽然已知PKC在理论上是优越的，但还没有已知的算法可以有效地计算PKC估计。由于校准被用来弥合计算机模拟和物理实验之间的差距，这项工作可能具有潜在的重大意义。在这个项目中取得的理论和技术进步可以通过期刊出版物、学生互访和在跨学科会议上的陈述等方式，帮助促进统计学、应用数学和概率论之间的进一步互动。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。