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We consider the problem of estimating the set of all inputs that leads asystem to some particular behavior. The system is modeled by anexpensive-to-evaluate function, such as a computer experiment, and we areinterested in its excursion set, i.e. the set of points where the functiontakes values above or below some prescribed threshold. The objective functionis emulated with a Gaussian Process (GP) model based on an initial design ofexperiments enriched with evaluation results at (batch-)sequentially determinedinput points. The GP model provides conservative estimates for the excursionset, which control false positives while minimizing false negatives. Weintroduce adaptive strategies that sequentially select new evaluations of thefunction by reducing the uncertainty on conservative estimates. Following theStepwise Uncertainty Reduction approach we obtain new evaluations by minimizingadapted criteria. Tractable formulae for the conservative criteria are derived,which allow more convenient optimization. The method is benchmarked on randomfunctions generated under the model assumptions in different scenarios of noiseand batch size. We then apply it to a reliability engineering test case.Overall, the proposed strategy of minimizing false negatives in conservativeestimation achieves competitive performance both in terms of model-based andmodel-free indicators.

Adaptive Design of Experiments for Conservative Estimation of Excursion Sets