Calibration and Uncertainty Analysis for Computer Simulations with Multivariate Output

Model calibration entails the inference about unobservable modeling parameters based on experimental observations of system response. When the model being calibrated is an expensive computer simulation, special techniques such as surrogate modeling and Bayesian inference are often fruitful. In this work we show how the flexibility of the Bayesian calibration approach can be exploited in order to account for a wide variety of uncertainty sources in the calibration process. We propose a straightforward approach for simultaneously handling Gaussian and non-Gaussian errors, as well as a framework for studying the effects of prescribed uncertainty distributions for model inputs that are not treated as calibration parameters. Further, we discuss how Gaussian process surrogate models can be used effectively when simulator response may be a function of time and/or space (multivariate output). All of the proposed methods are illustrated through the calibration of a simulation of thermally decomposing foam.