Chevalier, Clément

2019, Marmin, Sébastien, Chevalier, Clément, Ginsbourger, David

2016-11-1, Ginsbourger, David, Baccou, Jean, Chevalier, Clément, Perales, Frédéric

2014, Chevalier, Clément, Bect, Julien, Ginsbourger, David, Vazquez, Emmanuel, Picheny, Victor, Richet, Yann

2013, Chevalier, Clément, Ginsbourger, David

2019, Chevalier, Clément, Martius, Olivia, Ginsbourger, David

2016-8-2, Azzimonti, Dario, Bect, Julien, Chevalier, Clément, Ginsbourger, David

2014, Chevalier, Clément, Picheny, Victor, Ginsbourger, David

Several strategies relying on kriging have recently been proposed for adaptively estimating contour lines and excursion sets of functions under severely limited evaluation budget. The recently released R package KrigInv 3 is presented and offers a sound implementation of various sampling criteria for those kinds of inverse problems. KrigInv is based on the DiceKriging package, and thus benefits from a number of options concerning the underlying kriging models. Six implemented sampling criteria are detailed in a tutorial and illustrated with graphical examples. Different functionalities of KrigInv are gradually explained. Additionally, two recently proposed criteria for batch-sequential inversion are presented, enabling advanced users to distribute function evaluations in parallel on clusters or clouds of machines. Finally, auxiliary problems are discussed. These include the fine tuning of numerical integration and optimization procedures used within the computation and the optimization of the considered criteria.

2019, Azzimonti, Dario, Ginsbourger, David, Chevalier, Clément, Bect, Julien, Richet, Yann

2015, Chevalier, Clément, Emery, Xavier, Ginsbourger, David

Gaussian random field (GRF) conditional simulation is a key ingredient in many spatial statistics problems for computing Monte-Carlo estimators and quantifying uncertainties on non-linear functionals of GRFs conditional on data. Conditional simulations are known to often be computer intensive, especially when appealing to matrix decomposition approaches with a large number of simulation points. This work studies settings where conditioning observations are assimilated batch sequentially, with one point or a batch of points at each stage. Assuming that conditional simulations have been performed at a previous stage, the goal is to take advantage of already available sample paths and by-products to produce updated conditional simulations at minimal cost. Explicit formulae are provided, which allow updating an ensemble of sample paths conditioned on n≥0 observations to an ensemble conditioned on n+q observations, for arbitrary q≥1. Compared to direct approaches, the proposed formulae prove to substantially reduce computational complexity. Moreover, these formulae explicitly exhibit how the q new observations are updating the old sample paths. Detailed complexity calculations highlighting the benefits of this approach with respect to state-of-the-art algorithms are provided and are complemented by numerical experiments.

2014, Ginsbourger, David, Baccou, Jean, Chevalier, Clément, Perales, Frédéric, Garland, Nicolas, Monerie, Yann

Given a function depending both on decision parameters and nuisance variables, we consider the issue of estimating and quantifying uncertainty on profile optima and/or optimal points as functions of the nuisance variables. The proposed methods are based on interpolations of the objective function constructed from a finite set of evaluations. Here the functions of interest are reconstructed relying on a kriging model but also using Gaussian random field conditional simulations that allow a quantification of uncertainties in the Bayesian framework. Besides this, we introduce a variant of the expected improvement criterion, which proves efficient for adaptively learning the set of profile optima and optimizers. The results are illustrated with a toy example and through a physics case study on the optimal packing of polydisperse frictionless spheres.