Exploring and Solidifying Functional Calibration of Computer Models

当物理实验费用昂贵、时间密集或可能危害公众健康或环境时，科学家和工程师依靠计算机模型来研究复杂的物理系统。例如，计算机模型被用来预测大型风力涡轮机叶片的性能，估计疏散燃烧的建筑物的时间，以及模拟核燃料的导热系数。计算机模型校准是将计算机模型输出与物理数据进行比较，以便调整模型以尽可能真实地反映现实的过程。这个项目将探索一种被称为功能校准的校准版本，其中校准输入的适当值会随着不同的实验设置而变化。这项研究将为从业者配备基础良好的工具，帮助他们更好地了解他们正在研究的系统。有了这些工具，从业者可以改进计算机代码，做出更准确的预测。此外，该项目将为研究生和未被充分代表的少数群体提供机会，参与统计学、应用数学和工程学交叉领域的创新研究。首席研究员(PI)的目标是为功能计算机模型校准开发新的贝叶斯模型、理论和算法。第一个目标是使用变量选择文献中的工具来区分函数参数和常量，并在校准参数具有物理意义时学习新的物理。该项目还寻求在存在模型偏差的情况下更完整地表征函数参数的可辨识性。可辨识性工作将包括所谓的“混合”校准，即计算机模型同时包含常量和函数参数、最优基函数表示法和相关的渐近性。PI将从无限维的角度而不是离散化的角度研究参数，允许在推导可辨识性的充分必要条件时使用变分，并提供对有限维处理将遗漏的性质的洞察。此外，PI将与Kennedy-O‘Hagan模型、正交先验、比例高斯过程和校准方法的相关进展相结合，并在活动子空间方面取得进展，以促进使用超高维模型进行可行和有意义的校准。这些方法将在模拟环境和模型中进行说明，例如，材料的塑性变形和建筑能源使用。PI将开发与现有包兼容的软件，从而最大限度地提高这项工作的可及性和影响。该项目由统计计划和既定的激励竞争性研究计划(EPSCoR)共同资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Scientists and engineers rely on computer models to study complex physical systems when physical experiments are financially expensive, time-intensive, or potentially harmful to public health or the environment. For example, computer models are used to predict the performance of large wind turbine blades, estimate the time to evacuate burning buildings, and model thermal conductivity for nuclear fuels. Computer model calibration is the process of comparing computer model output to physical data so that the model can be tuned to represent reality as faithfully as possible. This project will explore a version of calibration known as functional calibration, in which the appropriate values of the calibration inputs change with different experimental settings. This research will equip practitioners with well-grounded tools to help them better understand the systems they are studying. With these tools, practitioners can improve computer codes and make more precise predictions. Further, this project will provide opportunities for graduate students and under-represented minorities to participate in innovative research at the intersection of statistics, applied mathematics, and engineering.The principal investigator (PI) aims to develop novel Bayesian models, theory, and algorithms for functional computer model calibration. The first aim is to use tools from the variable selection literature to distinguish functional parameters from constants and to learn new physics when calibration parameters have physical meaning. The project also seeks to characterize the identifiability of functional parameters more completely in the presence of model bias. The identifiability work will encompass the so-called “mixed” calibration in which a computer model contains both constant and functional parameters simultaneously, optimal basis function representations, and relevant asymptotics. The PI will study the parameters from the infinite-dimensional perspective rather than with discretization, allowing for the use of the calculus of variations when deriving necessary and sufficient conditions for identifiability, as well as providing insight into properties that would be missed with a finite-dimensional treatment. Further, the PI will wed the Kennedy-O’Hagan model, orthogonal priors, scaled Gaussian processes, and related advents to calibration methodology, with advances in active subspaces to facilitate feasible and meaningful calibration with extremely high-dimensional models. The methods will be illustrated in both simulated settings and models of, for example, plastic deformation of materials and building energy use. The PI will develop software compatible with existing packages, thereby maximizing the accessibility and impact of this work. This project is jointly funded by the Statistics Program and the Established Program to Stimulate Competitive Research (EPSCoR).This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.