Topics in Computer Experiments

这个项目将研究在计算机和物理实验的设计中出现的问题，并分析它们的输出。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差来源。模拟投入产出关系的计算机代码越来越多地用于代替物理实验，或者与物理实验结合使用，因为它们可以缩短制成品工程设计的交货时间，也可以在不同的现场使用条件和不同的制造条件下评估设计。一般来说，通过结合使用计算机和物理实验，可以对产品和工艺性能有更深入的了解。然而，计算机代码提供的投入产出关系的测量是有偏差的，因为在其开发过程中不可避免地使用了不足的物理或生物学。这一建议将解决上述挑战所产生的下列问题。1. 提高筛选方法的计算效率，以识别计算机代码中最重要的输入。2. 根据场输入的分布，开发估计计算机代码输出的上（或下）百分位数的方法。3. 估计多元计算机输出的帕累托最优输入值集合，以及相应的帕累托最优输入对应的输出向量的帕累托边界。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谐输入，包括那些混合定量和定性输入。使用计算机代码进行实验建模在工程、生物力学、物理科学、生命科学、经济学和其他自然科学领域（如气候变化评估和宇宙学）越来越普遍。在过去的二十年里，计算机代码作为实验工具的使用变得越来越复杂，因为输入代码的数量稳步增加，代码所体现的细节水平也在不断提高。研究人员现在既可以改变“工程”输入，也可以改变模型中描述操作条件的输入。此外，更详细的投入产出关系数学模型以及这些模型更精确的数值解往往会产生单次运行需要5-24小时的代码。此外，经常使用多种代码来描述正在研究的现象的不同方面。本项目将研究涉及此类计算机代码的实验设计中出现的问题，包括筛选此类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等问题，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.