Adaptive experimental design for multi‐fidelity surrogate modeling of multi‐disciplinary systems

Abstract

AbstractWe present an adaptive algorithm for constructing surrogate models of multi‐disciplinary systems composed of a set of coupled components. With this goal we introduce “coupling” variables with a priori unknown distributions that allow surrogates of each component to be built independently. Once built, the surrogates of the components are combined to form an integrated‐surrogate that can be used to predict system‐level quantities of interest at a fraction of the cost of the original model. The error in the integrated‐surrogate is greedily minimized using an experimental design procedure that allocates the amount of training data, used to construct each component‐surrogate, based on the contribution of those surrogates to the error of the integrated‐surrogate. The multi‐fidelity procedure presented is a generalization of multi‐index stochastic collocation that can leverage ensembles of models of varying cost and accuracy, for one or more components, to reduce the computational cost of constructing the integrated‐surrogate. Extensive numerical results demonstrate that, for a fixed computational budget, our algorithm is able to produce surrogates that are orders of magnitude more accurate than methods that treat the integrated system as a black‐box.