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

FRG：协作研究：统计建模、预测和计算机实验设计的创新

• 批准号: 1564376
• 负责人: Peter Chien
• 金额: $ 29.93万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1564376&HistoricalAwards=false
• 关键词: FRG; Collaborative; Research; Innovations; Statistical

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.

在过去的15年里，计算机模拟器的爆炸性增长促进了科学、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模拟器的运行来详细探索科学设计的替代方案，可能还会结合传统物理系统实验的运行。这项研究项目将推进使用计算机模拟器的实验的统计建模、设计和分析。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，这些模型将允许在模拟器提供物理系统性能的相关多变量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(一个输出的知识不提供关于其他输出的信息)，要么线性依赖于一组常见的潜在驱动因素。第二个研究领域涉及仿真方面的进展：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仿真器，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，当输出满足这一条件时，预测的响应在输入的排列下应该是恒定的；该项目将量化不变预测器中的不确定性。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上合理的方法的不确定性。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，以最大限度地减少确定模拟器输出对其每个输入的灵敏度所需的计算工作量。这项研究将为使用计算机模拟器的实验的建模、设计和分析建立一个统计框架。具体目标是(1)为具有多变量输出的计算机模拟器设计灵活的插补随机模型；(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当输出由点和集成响应组成时；(3)开发模拟器输出的仿真器，其包含模拟器响应中存在的相同不变性；(4)为昂贵的计算机代码量化L2校准预测器的不确定性；以及(5)构造新的切片拉丁超立方体设计，以允许高效地计算全局敏感性指数。研究人员将开发新的模式，培养对工程应用感兴趣的统计学研究生。将为专题专家创造机会，在三个领域提出关键的实际挑战：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。