An efficient methodology for modeling complex computer codes with Gaussian processes

Abstract

Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this inconvenience consists in replacing the complex computer code by a reduced model, called a metamodel, or a response surface that represents the computer code and requires acceptable calculation time. One particular class of metamodels is studied: the Gaussian process model that is characterized by its mean and covariance functions. A specific estimation procedure is developed to adjust a Gaussian process model in complex cases (non linear relations, highly dispersed or discontinuous output, high dimensional input, inadequate sampling designs, etc.). The efficiency of this algorithm is compared to the efficiency of other existing algorithms on an analytical test case. The proposed methodology is also illustrated for the case of a complex hydrogeological computer code, simulating radionuclide transport in groundwater.

A Kriging and Stochastic Collocation ensemble for uncertainty quantification in engineering applications

“…Note that, at any unknown point x in the design space, a Kr model estimates a predictive Gaussian distribution with mean (output response) and variance (uncertainty) [38]. Now building a reasonably accurate model requires an appropriate choice of the correlation function and its hyperparameters.…”

“…Moreover, various systematic sampling schemes exist to improve the Kr approximation, such as based on maximizing the variance [40], expected improvement which is purely used for optimization [41]. For a detailed derivation of the Kr method readers may refer to [38].…”

OpenTURNS: An Industrial Software for Uncertainty Quantification in Simulation

“…Kriging (also known as Gaussian process regression) [33,37,30,24] is a Bayesian technique that aims at approximating functions (most often in order to surrogate them because they are expensive to evaluate). In the following it is assumed the aim is to …”

Development of a methodological framework for the assessment of seismic induced tsunami hazard through uncertainty quantification: application to the Azores-Gibraltar Fracture Zone

“…The meta-model solution is a current engineering practice for estimating sensitivity indices . In this study, we use the Gaussian process meta-model (also called kriging) (Sacks et al., 1989), which good predictive capacities have been demonstrated in many practical situations (see (Marrel et al, 2008) for example). As a consequence, kriging meta-model will be useful both for sensitivity analysis and for a numerical database construction through uncertainty quantification (as reported in the next section).…”