Exploring and Solidifying Functional Calibration of Computer Models

Clemson University, Clemson SC

Investigators

Abstract

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.