Bayesian adaptive reconstruction of profile optima and optimizers

David Ginsbourger (1, 2) , Jean Baccou (3) , Clément Chevalier (1, 2) , Frédéric Perales (3, 4) , Nicolas Garland (3) , Yann Monerie (5)

1 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 IRSN - Institut de Radioprotection et de Sûreté Nucléaire
4 IRSN/DPAM/SEMCA/LEC - Laboratoire d'Etude du Combustible
5 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 base 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 field conditional simulations, that allow a quantification of uncertainties in the Bayesian framework. Besides, we elaborate a variant of the Expected Improvement criterion, that proves efficient for adaptively learning the set of profile optima and optimizers. The results are illustrated on 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 Simulations; Active Learning; Expected Improvement

Domaines: Modélisation et simulation; Statistiques [math.ST]; Théorie [stat.TH]; Analyse numérique [math.NA]; Machine Learning [stat.ML]; Applications [stat.AP]; Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

David Ginsbourger, Jean Baccou, Clément Chevalier, Frédéric Perales, Nicolas Garland, et al.. Bayesian adaptive reconstruction of profile optima and optimizers. 2013. ⟨hal-00920154⟩