Bayesian Adaptive Reconstruction of Profile Optima and Optimizers

David Ginsbourger (1) , Jean Baccou (2) , Clément Chevalier (1) , Frédéric Perales (2) , Nicolas Garland (2) , Yann Monerie (3)

1 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]
2 IRSN - Institut de Radioprotection et de Sûreté Nucléaire
3 ThM2 - ThermoMécanique des Matériaux

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.

Mots clés: robust design; Gaussian process regression; uncertainty quantification; conditional simulation; active learning; expected improvement

Domaines: Mécanique [physics.med-ph]; Traitement du signal et de l'image [eess.SP]

David Ginsbourger, Jean Baccou, Clément Chevalier, Frédéric Perales, Nicolas Garland, et al.. Bayesian Adaptive Reconstruction of Profile Optima and Optimizers. SIAM/ASA Journal on Uncertainty Quantification, 2014, 2 (1), pp.490-510. ⟨10.1137/130949555⟩. ⟨hal-02031714⟩