Universal Prediction Distribution for Surrogate Models

Malek Ben Salem (1, 2, 3, 4, 5, 6) , Olivier Roustant (2, 3, 4, 5, 6) , Fabrice Gamboa (7) , Lionel Tomaso (1)

1 ANSYS France
2 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
4 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
5 FAYOL-ENSMSE - Institut Henri Fayol
6 FAYOL-ENSMSE - Département Génie mathématique et industriel
7 IMT - Institut de Mathématiques de Toulouse UMR5219

The use of surrogate models instead of computationally expensive simulation codes is very convenient in engineering. Roughly speaking, there are two kinds of surrogate models: the deterministic and the probabilistic ones. These last are generally based on Gaussian assumptions. The main advantage of probabilistic approach is that it provides a measure of uncertainty associated with the surrogate model in the whole space. This uncertainty is an efficient tool to construct strategies for various problems such as prediction enhancement, optimization or inversion. In this paper, we propose a universal method to define a measure of uncertainty suitable for any surrogate model either deterministic or probabilistic. It relies on Cross-Validation (CV) sub-models predictions. This empirical distribution may be computed in much more general frames than the Gaussian one. So that it is called the Universal Prediction distribution (UP distribution). It allows the definition of many sampling criteria. We give and study adaptive sampling techniques for global refinement and an extension of the so-called Efficient Global Optimization (EGO) algorithm. We also discuss the use of the UP distribution for inversion problems. The performances of these new algorithms are studied both on toys models and on an engineering design problem.

Mots clés: Surrogate modeling; Bayesian optimization; Computer experiments

Domaines: Modélisation et simulation; Applications [stat.AP]; Statistiques [math.ST]

Malek Ben Salem, Olivier Roustant, Fabrice Gamboa, Lionel Tomaso. Universal Prediction Distribution for Surrogate Models. SIAM/ASA Journal on Uncertainty Quantification, 2017, 5 (1), pp.1086-1109. ⟨10.1137/15m1053529⟩. ⟨emse-01239789⟩