Combining field data and computer simulations for calibration and prediction

We develop a statistical approach for characterizing uncertainty in predictions that are made with the aid of a computer simulation model. Typically, the computer simulation code models a physical system and requires a set of inputs - some known and specified, others unknown. A limited amount of field data from the true physical system is available to inform us about the unknown inputs and also to inform us about the uncertainty that is associated with a simulation-based prediction. The approach given here allows for the following: uncertainty regarding model inputs (i.e., calibration); accounting for uncertainty due to limitations on the number of simulations that can be carried out; discrepancy between the simulation code and the actual physical system; uncertainty in the observation process that yields the actual field data on the true physical system. The resulting analysis yields predictions and their associated uncertainties while accounting for multiple sources of uncertainty. We use a Bayesian formulation and rely on Gaussian process models to model unknown functions of the model inputs. The estimation is carried out using a Markov chain Monte Carlo method. This methodology is applied to two examples: a charged particle accelerator and a spot welding process.