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)主要目标是为仅模拟器和模拟器+物理实验提供在广泛的目标函数中具有高预测效率的设计。实验设计将基于新的贝叶斯预测准则构建。(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模型的平均结构中的回归系数，将开发正则化先验，以及用于正则化控制相关函数的参数的新先验。(3)将开发批量顺序设计和分析方法，以确定控制变量的设置，以便在存在不可控制环境变量时最小化响应的平均值和可变性。(4)研究人员将开发方法来确定模拟器输出对混合定量-定性变量设置（包括非矩形输入应用）输入的灵敏度。(5)将为具有高维、非矩形区域（其边界只能用数值确定）的计算机代码设计构建空间填充设计的方法。例如，长尺度时间现象的计算模型，如气候和星系形成模型，其输入区域仅部分先验已知。复杂的物理和生物过程需要提供许多工程和科学领域的进步，越来越多地使用确定性计算机模拟器进行研究，这些模拟器由基于物理或生物学的数学模型编码而成。在许多这样的应用中，相关的物理实验数据也是可用的。这些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表现良好的系统。研究人员正在研究确定输入组合的有效方法，以便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，从这种联合实验中提取有关工程和科学问题的最大信息。研究人员开发的技术和成果用于研究人员参与的具体合作项目。其中包括以下应用：(a)组织工程，应力应变模拟器是设计特殊组织（如半月板替代品）过程的一部分，旨在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寿命；(c)减少注射成型应用中的收缩；(d)基于大气详细环流计算机模式的气候和天气预报。

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.