Évènements

The seventy-second UQSay seminar on UQ, DACE and related topics will take place **online** on Thursday afternoon, April 25, 2024.

This talk will present a surrogate-based framework for conservatively estimating risk from limited evaluations of an expensive physical experiment or simulation. Focus will be given to the computation of risk measures that quantify tail statistics of the loss, such as Average Value at Risk (AVaR). Monte Carlo (MC) sampling can be used to approximate such risk measures, however MC requires a large number of model simulations, which can make accurately estimating risk intractable for computationally expensive models. Given a set of samples surrogates are constructed such that the estimate of risk, obtained from the surrogate, is always greater than the empirical estimate obtained from the training data. These surrogates not only limit over-confidence in model reliability but produce estimates of risk that converge much faster to the true risk, than purely sampled based estimates.

The first part of the talk will discuss how to use the risk quadrangle, which rigorously connects stochastic optimization and statistical estimation, to construct conservative surrogates that can be tailored to the specific risk preferences of the model stakeholder. Surrogates constructed using least squares and quantile regression are specific cases of this framework. The second part of the talk will then present an approach, based upon stochastic orders, for constructing surrogates that are conservative with respect to families of risk measures, which is useful when risk preferences are difficult to elicit. This approach uses first and second order stochastic dominance to respectively enforce that the surrogate over-estimates probability of failure and AVaR for a finite set of thresholds. The conservative surrogates constructed introduce a bias that allows them to conservatively estimate risk. Theoretical results will be provided that show that for orthonormal models such as polynomial chaos expansions, this bias decays at the same rate as the root mean squared error in the surrogate. Numerous numerical examples will be used to confirm that that risk-aware surrogates do indeed overestimate risk while converging at the expected rate.

Reference: Surrogate modeling for efficiently, accurately and conservatively estimating measures of risk, RESS, 2022 – [github PyApprox].

Joint work with Drew Kouri (Sandia).

**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).

**Coordinators**: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

**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.