Design and analysis of 'noisy' computer experiments

Recently there has been a growing interest in using response surface techniques to expedite the global optimization of functions calculated by long running computer codes. The literature in this area commonly assumes that the objective function is a smooth, deterministic function of the inputs. Yet it is well known that many computer simulations -- especially those of computational fluid and structural dynamics codes -- often display what one might call 'numerical noise': rather than lying on a smooth curve, results appear to contain a random scatter about a smooth trend. This paper extends previous optimization methods based on the interpolating method of kriging to the case of such 'noisy' computer experiments. Firstly, we review how the kriging interpolation can be modified to filter out numerical noise. We then show how to adjust the estimate of the error in a kriging prediction so that previous approaches to optimization, such as the method of maximizing the expected improvement, continue to work effectively. We introduce the problems associated with noise and demonstrate our approach using computational fluid dynamics based problems