In order to reduce the time and resources devoted to design-space exploration during simulation-based design and optimization, the use of surrogate models, or metamodels, has been proposed in the literature. Key to the success of metamodeling efforts are the experimental design techniques used to generate the combinations of input variables at which the computer experiments are conducted. Several adaptive sampling techniques have been proposed to tailor the experimental designs to the specific application at hand, using the already-acquired data to guide further exploration of the input space, instead of using a fixed sampling scheme defined a priori. Though mixed results have been reported, it has been argued that adaptive sampling techniques can be more efficient, yielding better surrogate models with less sampling points. In this paper, we address the problem of adaptive sampling for single and multi-response metamodels, with a focus on Multi-stage Multi-response Bayesian Surrogate Models (MMBSM). We compare distance-optimal latin hypercube sampling, an entropy-based criterion and the maximum cross-validation variance criterion, originally proposed for one-dimensional output spaces and implemented in this paper for multi-dimensional output spaces. Our results indicate that, both for single and multi-response surrogate models, the entropy-based adaptive sampling approach leads to models that are more robust to the initial experimental design and at least as accurate (or better) when compared with other sampling techniques using the same number of sampling points.

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