Topics in Computer Experiments

这个项目将研究计算机和物理实验设计中出现的问题，并对它们的输出进行分析。物理实验是衡量投入产出关系的黄金标准，但这些测量包含噪声和可能无法识别的偏倚来源。模拟输入-输出关系的计算机代码越来越多地用于代替物理实验或与物理实验结合使用，因为它们可以减少制成品的工程设计以及在不同的现场使用条件和不同的制造条件下评估设计。一般而言，结合使用计算机和物理实验，可以更深入地了解产品和工艺性能。然而，计算机代码提供了一种对输入-输出关系的有偏见的测量，因为在它们的发展过程中不可避免地使用了不充分的物理学或生物学。该提案将解决因上述挑战而产生的下列问题。1.提高用于识别计算机代码的最重要输入的筛选方法的计算效率。2.制定一种方法，估计计算机代码输出相对于实地投入的分布的上(下)百分位数。3.估计多元计算机输出的Pareto最优输入值集合以及对应于Pareto最优输入的输出向量的Pareto前沿。4.开发统计方法，用于同时确定计算机模型的校准参数和调整输入，包括那些具有定量和定性混合输入的计算机模型。使用计算机代码的实验建模在工程学、生物力学、物理科学、生命科学、经济学以及其他自然科学领域，如气候变化和宇宙学的评估中，日益普遍。在过去的二十年里，计算机代码作为实验工具的使用已经变得越来越复杂，这是因为对这种代码的输入数量稳步增加以及代码所体现的详细程度。研究人员现在既可以改变“工程”输入，也可以改变描述模型中操作条件的输入。此外，输入-输出关系的更详细的数学模型以及这些模型的更精确的数值解通常会产生单次运行需要5-24小时的代码。此外，多个代码经常被用来描述被研究现象的不同方面。该项目将研究涉及这种计算机代码的实验设计中出现的问题，包括筛选这种代码的重要输入以确定重要输入，有效利用代码输出进行优化和其他问题，以及对相应的物理实验进行校准，以进一步提高其预测精度。

This project will study problems that occur in the design of computer and physical experiments and the analysis of their output. Physical experiments are the gold standard for measuring input-output relationships but these measurements that contain noise and possibly unrecognized sources of bias. Computer codes that model input-output relationships are used increasingly in place of, or in conjunction with, physical experiments because of they can provide decreased lead times in the engineering design of manufactured goods as well as for the assessment of designs in varying field-use conditions and varying conditions of fabrication. In general a deeper understanding of product and process performance can be made by using a combination of computer and physical experiments. However, computer codes provide a biased measurement of input-output relationships because of the inevitably inadequate physics or biology used in their development. This proposal will address the following problems that arise from the challenges sketched above. 1. To increase the computational efficiency of screening methodology for identifying the most important inputs to a computer code. 2. To develop methodology for estimating the upper (or lower) percentile of a computer code output with respect to the distributionof the field inputs. 3. To estimate the set of Pareto optimal input values for multivariate computer output and the corresponding Pareto Frontier of output vectors corresponding to the Pareto optimal inputs. 4. To develop statistical methodology for simultaneous determination of calibrationparameters and tuning inputs for computer models, including those with mixed quantitative and qualitative inputs.Experimental modeling using computer codes is increasingly prevalent in engineering, in biomechanics, in the physical sciences, in the life sciences, in economics, and other areas of natural science such as the assessment of climate change and cosmology. Over the past twenty years, the use of computer codes as experimental tools has become increasingly sophisticated due to the fact that the number of inputs to such codes has steadily increased as well as the level of detail embodied by the codes. Researchers can now vary both ``engineering'' inputs as well as inputs that describe the operating conditions in the model. In addition, more detailed mathematical models of the input-output relationship as well as more accurate numerical solution of these models often produce codes that require 5-24 hours for a single run. In addition, multiple codes are often used to describe different aspects of the phenomenon being studied. This project will study problems that occur in the design of experiments involving such computer codes including screening the important inputs to such codes to determine important inputs, the efficient use of code output for optimization and other problems, and the calibration of corresponding physical experiments to further improve their prediction accuracy.