Yann Richet

Quantile-Based Optimization of Noisy Computer Experiments With Tunable Precision

This article addresses the issue of kriging-based optimization of stochastic simulators. Many of these simulators depend on factors that tune the level of precision of the response, the gain in accuracy being at a price of computational time. The contribution of this work is two-fold: first, we propose a quantile-based criterion for the sequential design of experiments, in the fashion of the classical expected improvement criterion, which allows an elegant treatment of heterogeneous response precisions. Second, we present a procedure for the allocation of the computational time given to each measurement, allowing a better distribution of the computational effort and increased efficiency. Finally, the optimization method is applied to an original application in nuclear criticality safety. This article has supplementary material available online. The proposed criterion is available in the R package DiceOptim.

Fast Parallel Kriging-Based Stepwise Uncertainty Reduction With Application to the Identification of an Excursion Set

Stepwise uncertainty reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function  f in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of f above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. In this article we introduce several multipoint sampling criteria, allowing the selection of batches of points at which f can be evaluated in parallel. Such criteria are of particular interest when f is costly to evaluate and several CPUs are simultaneously available. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.

Global Sensitivity Analysis with 2D Hydraulic Codes: Application on Uncertainties Related to High-Resolution Topographic Data

Technologies such as aerial photogrammetry allow production of 3D topographic data including complex environments such as urban areas. Therefore, it is possible to create High-Resolution (HR) Digital Elevation Models (DEM) incorporating thin above-ground elements influencing overland flow paths. Although this category of “big data” has a high level of accuracy, there are still errors in measurements and hypothesis under DEM elaboration. Moreover, operators look for optimizing spatial discretization resolution in order to improve flood model computation time. Errors in measurement, errors in DEM generation, and operator choices for inclusion of this data within 2D hydraulic model, might influence the results of flood model simulations. These errors and hypothesis may influence significantly the flood modeling results variability. The purpose of this study is to investigate uncertainties related to (i) the own error of high-resolution topographic data and (ii) the modeler choices when including topographic data in hydraulic codes. The aim is to perform a Global Sensitivity Analysis (GSA) which goes through a Monte-Carlo uncertainty propagation, to quantify impact of uncertainties, followed by “Sobol” indices computation, to rank influence of identified parameters on result variability. A process using a coupling of an environment for parametric computation (Promethee) and a code relying on 2D shallow water equations (FullSWOF_2D) has been developed (P-FS tool). The study has been performed over the lower part of the Var river valley using the estimated hydrograph of a 1994 flood event. HR topographic data has been made available for the study area, which is 17.5 km2, by Nice municipality. Three uncertain parameters were studied: the measurement error (var. E), the level of details of above-ground element representation in DEM (buildings, sidewalks, etc.) (var. S), and the spatial discretization resolution (grid cell size for regular mesh) (var. R). Parameter var. E follows a probability density function, whereas parameters var. S and var. R are discrete operator choices. Combining these parameters, a database of 2,000 simulations has been produced using P-FS tool implemented on a high-performance computing structure. In our study case, the output of interest is the maximal water surface reached during simulations. A stochastic sampling on the produced result database has allowed to perform a Monte-Carlo approach. Sensitivity index have been produced at given points of interest, enhancing the relative weight of each uncertain parameters on variability of calculated overland flow. Perspectives for Sobol index maps production are brought to light.