Multi-fidelity information fusion based on prediction of kriging

Multifidelity surrogate modeling based on radial basis functions

“…Thus, Kriging models have recently been improved to take advantage of the use of both the coarse and the precise versions of the computer simulation, resulting in an enhanced prediction accuracy at a reduced computational cost (Kennedy and O'Hagan 2000). Then, several studies dealing with co-kriging (multifidelity version of Kriging) and its use in optimization have been exposed (Forrester et al 2007;Dong et al 2015;Le Gratiet and Cannamela 2015). Another possible choice in this context is the Radial Basis Functions (RBF) based interpolation method (Powell 1987;Dyn et al 1986).…”

Multiscale modeling of multimaterial systems using a Kriging based approach

“…Among the different metamodeling techniques tested, viz. stochastic collocation techniques [54,55], radial basis functions [56][57][58][59][60] and the Kriging family of methods, the Dynamic Kriging Method [36,37] (DKG) emerged as the best approach. DKG was shown to converge monotonically for several model closure laws even when the number of input points were low.…”

“…The MBKG method [56,57] assumes the inputs come from a stationary Gaussian random process, with a mean value of Pλ + Z and variance σ 2 β, i.e.…”

“…Using Equations (35) through (38), the joint posterior distribution for the MBKG formulation given in Equation (34) (57) The full conditionals for each of the model parameters, shown in [56], may be used to estimate the values of the model parameter for each MCMC sample. Because the MBKG method is evaluated using posterior distributions, the MBKG surrogate model is not a deterministic surrogate model but rather a surrogate that produces posterior distributions for the MBKG parameters.…”

“…Because the metamodel in [42] was created from expensive numerical computations, particular attention was paid to the selection of a suitable metamodeling technique. Among a variety of methods evaluated [42,52] it was found that a variant of the Kriging method [48,[53][54][55], the Modified Bayesian Kriging Method (MBKG) [56,57] constructed accurate and smooth surrogates from a minimum number of mesoscale simulations. The MBKG method was used to construct surrogates for the drag on particle clusters as a function of Mach Number,…”