### Department of Industrial Engineering and Management Sciences, Northwestern University

## Enhancing Stochastic Kriging Metamodels for Computer Simulation

##### Thursday, January 12, 3:30 PM

##### Room G31 Benedum Hall

**Abstract: **When systems are relatively complex or intense simulation is necessary to evaluate even one scenario, simulation models are not capable to support decision making in a timely manner. Metamodels, if well-constructed, can provide an accurate approximation to the real simulation output as if the simulation can be run “on demand” with the given decision variables, and hence greatly facilitate real-time decision making. Stochastic kriging is a new metamodeling technique proposed for effectively representing the mean response surface implied by a stochastic simulation; it takes into account both stochastic simulation noise and uncertainty about the underlying response surface of interest. In this talk, upon setting up the framework of stochastic kriging, we first discuss the adverse effect of common random numbers (CRN, a variance reduction technique widely used in stochastic simulation) on prediction when being used with stochastic kriging metamodels. We then focus on the enhanced stochastic kriging metamodels with gradient estimators and show that incorporating gradient estimators into stochastic kriging tends to significantly improve surface prediction. To address the important issue of which type of gradient estimator to use, we briefly review stochastic gradient estimation techniques and elaborate on the properties of the infinitesimal perturbation analysis (IPA) and likelihood ratio/score function (LR/SF) gradient estimators when incorporated into stochastic kriging metamodels and make recommendations.