GPs are used as metamodels in sensitivity analysis for traffic simulation models by Ciuffo et al. Gidaris and Taflanidis ( 2015) use kriging for earthquake engineering to see how the configuration of fluid viscous dampers affects costs. ( 2012) their metamodels predict the “nitrogen dioxide ( N 2 O) fluxes and nitrogen leaching from European farmlands.” GPs are used for metamodeling in simulations for corn crops by Villa-Vialaneix et al. ( 2014) model the current density of lithium-ion batteries as a function of eight input parameters. ( 2014) use these models in materials science for modeling functionally graded foam-filled tapered tubes to see which designs have the best energy absorption characteristics.ĭu et al. The GP model allows them to perform global sensitivity analysis to see which parameters in their acoustic model affect the transmission. ( 2014) use GPs to model the acoustic transmission on launchers in an effort to reduce damage to the payload. Our goal is to determine which software packages have the capability of effectively and reliably estimating locations for new design points by estimating the metamodel and its prediction error.įor example, in aerospace design, Christen et al. However, for building an accurate global metamodel, the response information can be used to select design points where the prediction error is estimated to be large or locations that would help estimate the metamodel parameters more accurately. If the objective is to find the location of an optimum,Īdaptive designs are vastly more efficient because they can select locations where the response is likely to be desirable.
An adaptive sequential experiment design uses not only the location of the previous design points, but also the observed value of the response at those design points. A sequential experiment design is called non-adaptive if the location of each additional design point is related only to the location of the previous design points in the input space. We think of the sequential selection of these design points as a sequential experiment design. In addition to its use as a stopping criterion, prediction error estimates can be used by a sequential algorithm to determine the location of the next set of design points to run with the actual computer simulation model. This is where the model-based estimate of GP fitting is very attractive. Many fitting methods, such as splines and neural networks, provide no estimate of prediction error apart from extrinsic methods like cross validation which are not related to the fitted model itself. Sequential algorithms require a stopping criterion.įor building an accurate global metamodel, a stopping criterion that is a function of the estimated prediction error makes sense. In many applications, random noise or computational limitations do not allow for extrinsic measures of prediction accuracy, and thus an easily obtained estimate of the uncertainty of prediction is valuable if it is at least reasonably accurate. Since GP fitting is often used over other fitting techniques because of its model-based estimate of prediction error, the quality of a software implementation depends not only on the accuracy of the fitted surface, but also the accuracy of the error predictions. So, in practice, different packages can give substantially different results. Most GP fitting packages use essentially the same equations, but there is variability in how parameters are defined and estimated through numerical optimization. GP fitting is unlike linear regression where, for a given data set, all software packages will produce exactly the same parameter estimates and fitted surface (up to round-off error). Many practitioners are not familiar with the particulars of GP fitting, so we investigate packages that are relatively easy to use and do not require extensive knowledge of all the options and parameters that can be specified. In this paper we are concerned with how GP models are used by practitioners, so we compare the performance of some commonly used software packages.
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