Monday, January 31, 2022

UQSay #42

The forty-second UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, February 3, 2022.

2–3 PM — Pietro Congedo (Inria, CMAP, Ecole Polytechnique, IPP) — [slides]

Optimization under Uncertainty of Large Dimensional Problems using Quantile Bayesian Regression

Robust optimization strategies typically aim at minimizing some statistics of the uncertain objective function and can be expensive to solve when the statistic is costly to estimate at each design point. Surrogate models of the uncertain objective function can be used to reduce this computational cost. However, such surrogate approaches classically require a low-dimensional parametrization of the uncertainties, limiting their applicability. This work concentrates on the minimization of the quantile and the direct construction of a quantile regression model over the design space, from a limited number of training samples. A Bayesian quantile regression procedure is employed to construct the full posterior distribution of the quantile model. Sampling this distribution, we can assess the estimation error and adjust the complexity of the regression model to the available data. The Bayesian regression is embedded in a Bayesian optimization procedure, which generates sequentially new samples to improve the determination of the minimum of the quantile. Specifically, the sample infill strategy uses optimal points of a sample set of the quantile estimator. The optimization method is tested on simple analytical functions to demonstrate its convergence to the global optimum. The robust design of an airfoil’s shock control bump under high-dimensional geometrical and operational uncertainties serves to demonstrate the capability of the method to handle problems with industrial relevance. Finally, we provide recommendations for future developments and improvements of the method.

Joint work with C. Sabater, S. Goertz, O. Le Maître, T. Bourdais.

Ref: DOI:10.1016/j.cma.2020.113632.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S).

Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.