MascotNum2014 conference- Multi-fidelity regression using a non-parametric relationship.

We study the synthesis of data from different experiments. These experiments are very complex com-puter simulations that take several hours to produce a response for a given input. Understanding the phenomenon modeled by the simulation requires a large number of responses and in practice having all of them is unfeasible due to time constraints. This is why the computer simulation is often replaced by a simpler probabilistic model, also known as metamodel, that is faster to run. The studied metamodel is based on the hypothesis that the computer simulation is in fact the realization of a gaussian process indexed by the inputs and defined by a parametric mean function and a parametric covariance function. A small number of responses produced by the computer code are used to determine the values of the parameters of the mean and covariance functions. Given a new input, the predicted value is the expectation of the stochastic process at that input conditioned by the responses available. Since the stochastic process is gaussian, there is a formula for this expectation and the error of prediction. When the precision of the output produced by the computer code can be tuned it is possible to incorporate responses with different levels of fidelity to enhance the prediction of the most accurate simulation at a new input while respecting the time constraints. This is usually done by adding several imprecise responses instead of a few precise ones. The main example for this type of computer experiments ar