Complex Experiments and High-Input Simulators: Challenges in Design, Prediction and Sensitivity

调查人员研究了五个问题领域。(1)一个主要目标是为仅用于模拟器和模拟器+物理实验的广泛类别的目标函数提供具有高预测效率的设计。实验设计将基于一种新的贝叶斯预测标准。(2)研究人员将制定正则化先验，用于需要大量输入和稀疏采样的模拟器。特别是，对于非平稳GP模型，将为均值结构中的回归系数开发正则化先验，以及新的正则化先验，以正则化控制相关函数的参数。(3)将开发批量序贯设计和分析方法，以确定控制变量的设置，以便在存在不可控环境变量的情况下将响应的平均值和变异性降至最低。(4)调查人员将开发确定模拟器输出对混合定量-定性变量环境中输入的敏感性的方法，包括非矩形输入应用。(5)将为具有高维非矩形区域的计算机代码设计空间填充设计方法，这些区域的边界只能用数字确定。例如，气候和星系形成模型等长尺度时间现象的计算模型，其输入区域只是部分已知的优先事项。提供许多工程和科学领域的进步所需的复杂物理和生物过程越来越多地使用由基于物理或生物的数学模型编码的确定性计算机模拟器来研究。在许多这样的应用中，来自相关物理实验的数据也是可用的。这类研究的目标范围从在给定环境中优化系统性能到设计在各种环境中都能很好地运行的系统。研究人员正在研究确定输入组合的有效方法，以运行复杂的模拟器代码和相关的物理实验。他们还在开发方法，从这种联合实验中最大限度地提取有关工程和科学问题的信息。调查员开发的技术和结果用于调查员参与的具体合作项目。这些应用包括：(A)组织工程，应力应变模拟器是设计特殊组织过程的一部分，如半月板替代物，其目的是在患者群体中表现良好；(B)设计涂层系统，以延长摩擦学和磨损应用中机床的使用寿命；(C)减少注射成型应用中的收缩；(D)根据详细的大气循环计算机模型预测气候和天气。

The investigators study five problem areas. (1) A primary objective is to provide designs that have high predictive efficiency over a wide class of objective functions for simulator-only and simulator+physical experiments. Experimental designs will be constructed based on a new Bayesian prediction criterion. (2) The researchers will formulate regularization priors for use with simulators that require large numbers of inputs and are sampled sparsely. In particular, regularization priors will be developed for regression coefficients in the mean structure for non-stationary GP models as well as new priors to regularize the parameters controlling the correlation function. (3) Batch sequential design and analysis methodology will be developed to determine settings of control variables for minimizing the mean and variability of the response in the presence of non-controllable environmental variables. (4) The investigators will develop methods for determining the sensitivity of simulator outputs to inputs in mixed quantitative-qualitative variable settings, including non-rectangular input applications. (5) Methodology will be devised for constructing space-filling designs for computer codes with high-dimensional, non-rectangular regions whose boundaries can only be determined numerically. For example, computational models of long-scale temporal phenomena such as climate and galaxy formation models, have inputs regions are only partially known a priori.The complex physical and biological processes required to provide advances in many engineering and scientific fields are increasinglystudied using deterministic computer simulators coded from physics- or biology-based mathematical models. In many such applications, the data from related physical experiments are also available. The goals in such studies range from optimizing system performance in a given environment to designing systems that perform well in a wide variety of environments. The investigators are conducting research on efficient methods for determining input combinations at which to run complex simulator codes and associated physical experiments. They are also developing methods to extract the maximum information about the relevant engineering and scientific questions from such combined experiments. Techniques and results developed by the investigators are used in the specific collaborative projects in which the investigators participate. These include the following applications: (a) Tissue engineering where stress-strain simulators form part of the process of designing specialty tissues such as meniscal substitutes which are meant to perform well in a patient population; (b) Design of coating systems to extend the life of machine tools in tribological and wear applications; (c) Decreasing the shrinkage in injection molding applications; (d) Prediction of climate and weather based on detailed circulation computer models ofthe atmosphere.