Statistical Methods for Computer Model Parameter Calibration Based on Multi-fidelity Gaussian Process Emulators
DescriptionThis project will develop statistical methods that utilize a low-fidelity model to significantly reduce computation cost incurred in estimation of parameters in a high-fidelity model from given physical experiment data.Computer models of a physical system can come in different levels of fidelity. These models are often computer codes that implement numerical algorithms to solve partial differential equations (PDEs) to different levels of accuracy or computer codes that solve systems of PDEs of different levels of complexity. Typically, a high-fidelity model is more time consuming to solve than a low-fidelity model but provides higher prediction accuracy for the real system. For practical problems encountered in geophysical, biomedical, engineering mechanics, and many other applications, parameters in computer models are often uncertain and need to be estimated from data obtained via experiments or observations on the physical system. This class of problems is called inverse problems or parameter calibration problems. Due to the smaller numerical errors and model bias, parameter calibration performed with a high-fidelity model incurs less bias, which can furnish more accurate information to the model user. However, because solving inverse problems can require thousands of runs of the computer model, computational cost is a key consideration in choosing a method to solve inverse problems for a high-fidelity computer model.In this project, we shall develop new statistical methods that utilize one or more low-fidelity models that share the same calibration parameters as a high-fidelity model to reduce computational cost incurred in estimating parameters of the high-fidelity model.We shall link the high and low fidelity models with autoregressive Gaussian process (GP) models, which combines information from the computer models at different fidelity levels to improve prediction of the output of the model with highest fidelity. Expedient Bayesian inference procedures for parameter calibration based a few versions of this model for modeling functional and multiple outputs shall be developed. In addition, we shall also design computationally efficient algorithms specifically for Bayesian inference in large scale inverse problems (problems with a large set of measurements on the physical system observed over a space-time domain). Sequential Bayesian optimal design approaches to reduce the number of high-fidelity simulations for parameter estimation will be developed. Key issues such as the appropriate optimal design criteria to employ, techniques to compute the criteria efficiently and accurately, and expansion or contraction of the experiment region based on the posterior distribution of the calibration parameters shall be addressed.
|Effective start/end date||1/01/19 → …|