FRG: Collaborative Research: Innovations in Statistical Modeling, Prediction, and Design for Computer Experiments

在过去的15年里，计算机模拟器使用的爆炸式增长帮助激发了科学、工程和生物研究的革命，其中包括航空航天工业、材料科学、可再生能源和生物力学的进步。研究人员可以在广泛的操作环境下，使用物理系统的模拟器，可能与传统物理系统实验相结合，对科学设计方案进行详细的探索。这个研究项目将推进使用计算机模拟器的统计建模、设计和实验分析。第一个研究领域是模拟器输出的改进建模：研究人员将开发灵活的随机模型，以便在模拟器提供物理系统性能的相关多元输出的情况下进行更准确的预测。当前的预测模型要么假设输出独立性（一个输出的知识不提供关于其他输出的信息），要么假设对一组共同的潜在驱动因素的线性依赖。第二个研究领域涉及仿真的进展：研究人员的目标是为新的输入和输出设置设计有效的模拟器输出模拟器，例如当梯度信息可用时，或者当输出由点和综合测量组成时。他们计划构建包含模拟器输出中存在的自然不变性的预测器。例如，当输出满足该条件时，在输入的排列情况下，预测的响应应该是恒定的；该项目将量化不变预测因子中的不确定性。研究人员还计划量化最近一种基于物理实验数据校准计算机模拟器的理论证明方法的不确定性。第三个研究领域是模拟器实验的设计：将设计有效的模拟器实验设计，以尽量减少确定模拟器输出对每个输入的灵敏度所需的计算工作量。本研究将为使用电脑模拟器的实验建模、设计和分析建立一个统计框架。具体目标是：(1)为具有多元输出的计算机模拟器设计灵活的插值随机模型；(2)为新的输入和输出设置发明有效的预测器，例如当梯度信息可用时，或者当输出由点响应和综合响应组成时；(3)开发模拟器输出的模拟器，其中包含模拟器响应中存在的相同不变性；(4)量化昂贵计算机代码的L2校准预测器的不确定性；(5)构造新的拉丁超立方体切片设计，以实现全局灵敏度指标的高效计算。研究人员将开发培养对工程应用感兴趣的统计学研究生的新模式。将为学科专家创造机会，在三个领域提供关键的实践挑战：航空航天/机械工程、生物力学和材料科学，并与研究人员开展联合应用项目。

The explosive growth in the use of computer simulators in the last fifteen years has helped galvanize a revolution in scientific, engineering, and biological research that includes advances in the aerospace industry, material science, renewable energy, and biomechanics. Researchers can make a detailed exploration of scientific design alternatives under a wide set of operating environments using runs from a simulator of a physical system, possibly coupled with those from a traditional physical system experiment. This research project will advance the statistical modeling, design, and analysis of experiments that use computer simulators. The first research area is Improved Modeling of Simulator Output: The investigators will develop flexible stochastic models that will allow more accurate prediction in settings where the simulator provides related multivariate output of the performance of a physical system. Current prediction models either assume output independence (knowledge of one output gives no information about other outputs) or a linear dependence on a common set of latent drivers. The second research area concerns Advances in Emulation: The investigators aim to devise efficient emulators of simulator output for novel input and output settings such as when gradient information is available or when the output consists of both point and integrated measures. They plan to construct predictors that incorporate natural invariances present in the simulator output. For example, the predicted response should be constant under permutations of the inputs when the output satisfies this condition; the project will quantify the uncertainty in the invariant predictors. The investigators also plan to quantify the uncertainty of a recent, theoretically-justified method of calibrating computer simulators based on physical experimental data. The third research area is the Design of Simulator Experiments: Efficient designs of simulator experiments will be devised to minimize the computational effort required to determine the sensitivity of a simulator output to each of its inputs. This research will build a statistical framework for the modeling, design and analysis of experiments that employ computer simulators. The specific goals are (1) to devise flexible interpolating stochastic models for computer simulators with multivariate output; (2) to invent efficient predictors for novel input and output settings such as when gradient information is available or when the output consists of both point and integrated responses; (3) to develop emulators of simulator output that incorporate the same invariances present in the simulator responses; (4) to quantify the uncertainty of L2 calibrated predictors for expensive computer codes; and (5) to construct new sliced Latin hypercube designs to allow the efficient calculation of global sensitivity indices. The investigators will develop new modes for training statistics graduate students having interests in engineering applications. Opportunities will be created for subject matter specialists to provide critical practical challenges in three areas: aerospace/mechanical engineering, biomechanics, and material science, and to conduct joint applied projects with the researchers.