Uncertainty quantification and reduction for the monotonicity properties of expensive-to-evaluate computer models
Résumé
We consider the problem of estimating monotonicity properties of a scalar-valued numerical model---e.g., a finite element model combined with some post-processing. Several quantitative monotonicity indicators are introduced. Since the evaluation of the numerical model is usually time-consuming, these indicators have to be estimated with a small budget of evaluations. We adopt a Bayesian approach, where the numerical model itself is modeled as a Gaussian process. First, estimation of the monotonicity indicators, and quantification of the uncertainty surrounding them, are carried out using conditional simulations of the Gaussian processes derivatives. Then, the Sequential Uncertainty Reduction principle is used to design a sequential design strategy, to get improved knowledge of the monotonicity properties of the model. The approach is illustrated with a numerical model of a passive component in a power plant
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