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: 1564395
• 负责人: Thomas Santner
• 金额: $ 35.48万
• 依托单位: Ohio State University
• 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 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1564395&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.

在过去的十五年中，计算机模拟器使用的爆炸性增长有助于激发科学，工程和生物学研究的革命，其中包括航空航天行业的进步，材料科学，可再生能源和生物力学。研究人员可以使用物理系统的模拟器进行详细探索科学设计替代方案，并可能与传统物理系统实验中的模拟器进行运行。该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。第一个研究领域是改进模拟器输出的建模：研究人员将开发灵活的随机模型，这将在模拟器提供相关的物理系统性能的相关多元输出的设置中更准确的预测。当前的预测模型假设输出独立性（一个输出知识没有提供有关其他输出的信息），或者对一组通用潜在驱动程序的线性依赖性。第二个研究领域涉及仿真的进展：研究人员旨在为新颖的输入和输出设置（例如何时可用梯度信息或何时由点组成的梯度信息和集成度量）设计有效的模拟器输出模拟器。他们计划构建融合模拟器输出中存在的自然恒星的预测因子。例如，在输出满足此情况时，在输入的排列下，预测响应应恒定。该项目将量化不变预测变量的不确定性。研究人员还计划根据物理实验数据量化校准计算机模拟器的最新方法的不确定性。第三个研究领域是模拟器实验的设计：将设计模拟器实验的有效设计，以最大程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。这项研究将建立一个统计框架，用于对采用计算机模拟器的实验进行建模，设计和分析。特定目标是（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）为新颖的输入和输出设置（例如可用梯度信息或输出由点和集成响应组成时）发明有效的预测指标； （3）开发模拟器输出的模拟器，该模拟器输出包含模拟器响应中存在相同的不向导； （4）量化昂贵的计算机代码的L2校准预测变量的不确定性； （5）构建新切的拉丁超立方体设计，以有效地计算全球灵敏度指数。调查人员将开发新的模式，以培训统计研究生对工程应用有兴趣。将为主题专家创造机会，以在三个领域提供关键的实际挑战：航空/机械工程，生物力学和材料科学，并与研究人员进行联合应用项目。