The seventh UQSay seminar on Uncertainty Quantification and related
topics, organized by L2S
and MSSMAT, will take
place on Thursday afternoon,
**January 16**, 2020,
at CentraleSupelec Paris-Saclay (Eiffel building, amphi III).

We will have two talks:

Iterative estimation in uncertainty and sensitivity analysis

While building and using numerical simulation models, uncertainty and sensitivity analysis are invaluable tools. In engineering studies, numerical model users and modellers have shown high interest in these techniques that require to run many times the simulation model with different values of the model inputs in order to compute statistical quantities of interest (QoI, i.e. mean, variance, quantiles, sensitivity indices…). In this talk we will focus on new issues relative to large scale numerical systems that simulate complex spatial and temporal evolutions. Indeed, the current practice consists in the storage of all the simulation results. Such a storage becoming quickly overwhelming, with the associated long read time that makes cpu time consuming the estimation of the QoI. One solution consists in avoiding this storage and in computing QoI on the fly (also called in-situ). It turns the problem to considering problems of iterative statistical estimation. The general mathematical and computational issues will be posed, and a particular attention will be paid to the estimation of quantiles (via an adaptation of the Robbins-Monro algorithm) and variance-based sensitivity indices (the so-called Sobol' indices).

Joint work with Yvan Fournier (EDF), Bruno Raffin (INRIA), Alejandro Ribés (EDF), Théophile Terraz (INRIA).

Refs: hal-01607479 and hal-02016828.

Related software: Melissa.

Bayesian Multi-objective Optimization with Noisy Evaluations using the Knowledge Gradient

We consider the problem of multi-objective optimization in the case where each objective is a stochastic black box that provides noisy evaluation results. More precisely, let f_1, ..., f_q be q real-valued objective functions defined on a search domain 𝕏 ⊂ ℝ^d, and assume that, for each x ∈ 𝕏, we can observe a noisy version of the objectives: Z_1 = f_1(x) + ε_1, ..., Z_q = f_q(x) + ε_q, where the ε_i's are zero-mean random variables. Our objective is to estimate the Pareto-optimal solutions of the problem: min f_1, ..., f_q.

We adopt a Bayesian optimization approach, which is a classical approach when the affordable number of evaluations is severely limited. In essence, Bayesian optimization consists in choosing a probabilistic model for the outputs Z_i and defining a sampling criterion to select evaluation points in the search domain 𝕏. Here, we propose to discuss the extension of the Knowledge Gradient approach of Frazier, Powell and Dayanik (INFORMS J. Comput., 21(4):599–613, 2009) to multi-objective problems with noisy evaluations. For instance, such an extension has been recently proposed by Astudillo and Frazier.

Joint work with Julien Bect (L2S), Héloïse Baraffe (EDF), Juliette Morin (EDF), Gilles Malarange (EDF) and Emmanuel Vazquez (L2S).

Organizers: Julien Bect (L2S) and Fernando Lopez Caballero (MSSMAT).