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Communication Dans Un Congrès Année : 2015

Adaptive design for the estimation of high-variation regions using non-stationary Gaussian process models

Résumé

In the context of expensive deterministic simulations, Gaussian process (GP) models have become a standard device for sequential design of experiments. In this context, the objective function f is seen as a black box and assumed to be one realization of a GP with given mean and covariance. Sampling criteria can then be worked out to optimally choose the next evaluation points under the GP assumption. State of the art criteria notably include MSE and IMSE. Further criteria dedicated to localizing optima, and also to the estimation of target regions have been proposed. Here we propose two approaches for learning f in cases where it has very heterogeneous variations across the input space. First, we define a new family of criteria inspired by MSE and IMSE but with a focus on conditional gradients under the GP model. Second, we use the classic MSE and IMSE criteria with a specific GP model accounting for prior knowledge about the heterogeneous variations of f. All combinations of the considered criteria and GP models are compared on a test case from the French nuclear safety institute about the mechanical ageing of power plants. It is found on this application that in the case of stationary GP modelling, one of the proposed derivative-based criteria outperforms MSE and IMSE both in terms of local and global approximation error. However, the overall best results in terms of global approximation are obtained with IMSE and our non-stationary kernel.
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Dates et versions

hal-01402266 , version 1 (24-11-2016)

Identifiants

  • HAL Id : hal-01402266 , version 1

Citer

Sébastien Marmin, David Ginsbourger, Jean Baccou, Jacques Liandrat, Frédéric Perales. Adaptive design for the estimation of high-variation regions using non-stationary Gaussian process models. Eighth International Workshop on Simulation , Sep 2015, Vienne, Austria. ⟨hal-01402266⟩
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