Exploring and Solidifying Functional Calibration of Computer Models

科学家和工程师依靠计算机模型来研究复杂的物理系统，当物理实验在财政上昂贵，时间密集，或对公众健康或环境有潜在危害时。例如，计算机模型被用来预测大型风力涡轮机叶片的性能，估计疏散燃烧建筑物的时间，以及模拟核燃料的导热性。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的过程，以便调整模型以尽可能忠实地代表现实。本项目将探索一种称为功能校准的校准版本，其中校准输入的适当值随着不同的实验设置而变化。这项研究将为实践者提供基础良好的工具，帮助他们更好地理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并做出更精确的预测。此外，该项目将为研究生和少数族裔提供参与统计、应用数学和工程交叉领域创新研究的机会。首席研究员（PI）的目标是开发新的贝叶斯模型、理论和算法，用于功能计算机模型校准。第一个目的是利用变量选择文献中的工具来区分功能参数和常数，并在校准参数具有物理意义时学习新的物理。该项目还试图在存在模型偏差的情况下更完整地描述功能参数的可识别性。可识别性工作将包括所谓的“混合”校准，其中计算机模型同时包含常数和功能参数，最优基函数表示和相关的渐近。PI将从无限维的角度研究参数，而不是离散化，允许使用变分法在推导可识别性的必要和充分条件时，以及提供对有限维处理可能错过的特性的洞察。此外，PI将结合Kennedy-O 'Hagan模型、正交先验、缩放高斯过程和校准方法的相关进展，以及主动子空间的进步，以促进对极高维度模型的可行和有意义的校准。这些方法将在模拟设置和模型中进行说明，例如，材料的塑性变形和建筑能源使用。PI将开发与现有软件包兼容的软件，从而最大化这项工作的可访问性和影响。该项目由统计计划和促进竞争研究的既定计划（EPSCoR）共同资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.