A Statistical Framework for the Design and Analysis of Multi-Fidelity Computer Experiments

该奖项的研究目标是为此类模拟的设计、抽样和建模开发一个新的统计框架。多保真计算机建模正在成为研究工程中复杂系统的一种流行方法。该方法将大量的近似模拟与较少的详细模拟相结合，用于建立预测模型、校准和优化。这项研究将产生足够普遍的工具和技术，以适用于大量的工程问题，在这些问题中，有两种计算机模型可用，其中一种模型比另一种模型更准确，但成本更高。研究工作的重点是开发一种新的抽样方案来估计一组多保真计算机模拟的输出的期望值，一种新型的统计设计来有效地运行多保真计算机模拟，以及新的统计方法来建模具有定性和定量因素的多保真计算机模拟。来自行业和国家实验室的具有挑战性的真实问题将被用来测试和验证开发的结果。如果成功，这项研究的结果将为工程师提供一个统计指导的框架，用于高效地进行多保真计算机模拟。应用实例包括概念设计、电子冷却、水文学、冲击动力学、材料设计、纳米技术、石油储备管理、聚合物电解质燃料电池制造、热力学和车辆多体动力学。计算机模拟现在被广泛用于解决美国和世界面临的几个紧迫问题，如气候变化、能源节约和可再生/清洁能源创新。开发的结果将潜在地使这些关键领域的研究人员能够使用模拟来解决更大规模的问题。这项研究将以开源软件的形式传播，直接惠及多保真计算机实验的用户，并产生长期影响。研究生和本科生统计和工程专业的学生将通过参与研究和新课程的开设而受益。

The research objective of this award is to develop a new statistical framework for the design, sampling and modeling of such simulations. Multi-fidelity computer modeling is emerging as a popular method for studying complex systems in engineering. This method combines a large number of approximate simulations with a smaller number of detailed simulations for building prediction models, calibration and optimization. The research will result in tools and techniques which are general enough to apply to a large array of engineering problems in which two computer models are available and one model is more accurate but more expensive than the other. The research effort is focused on the development of a new sampling scheme for estimating the expected values of the outputs of a set of multi-fidelity computer simulations, a new type of statistical design for efficiently running multi-fidelity computer simulations and novel statistical methods for modeling multi-fidelity computer simulations with qualitative and quantitative factors. Challenging real-world problems from the industry and national labs will be used to test and validate the developed results.If successful, the results of this research will provide engineers a statistics-guided framework for efficiently conducting multi-fidelity computer simulations. Example applications include conceptual design, electronic cooling, hydrology, impact dynamics, material design, nanotechnology, oil reserve management, polymer electrolyte fuel cells manufacturing, thermal dynamics and vehicle multi-body dynamics. Computer simulations are now widely used for solving several pressing issues faced by the U.S. and the world such as climate change, energy conservation and renewable/clean energy innovation. The developed results will potentially enable researchers in these critical fields to use simulations to tackle problems of much larger scales. The research will be disseminated as open source software to directly benefit users of multi-fidelity computer experiments and make a long-term impact. Graduate and undergraduate statistics and engineering students will benefit through involvement in the research and new course offering.