Summer school CEA-EDF-INRIA 2017

Design and optimization under uncertainty of large-scale numerical models

Location: Université Pierre et Marie Curie, Jussieu, Paris

Dates: July, 3d to July, 7th

Secretary: Régis Vizet (CEA/DAM)

Scientific organizers : Bertrand Iooss (EDF R&D) and Guillaume Perrin (CEA/DAM)

Official link

When dealing with complex and cpu-time expensive computer codes, engineers and researchers have to adopt smart strategies in order to improve the robustness and the precision of their study results. Indeed, several uncertainties affect their physical and numerical models, the required solving algorithms and the various model input data and parameters.

The topic of dealing with uncertainty in numerical simulation is very broad. In 2005, a CEA-EDF-INRIA summer school has covered the basics of uncertainty propagation and sensitivity analysis with deterministic and stochastic approaches. In 2011, another CEA-EDF-INRIA summer school has explained several mathematical concepts of VV&UQ (validation, verification and uncertainty quantification), by using in particular Bayesian techniques.

This summer school aims to cover techniques devoted to optimization goals, by taking into account the remaining uncertainties. Indeed, one of the main difficulties stands on cpu-time expensive numerical models subject to environmental uncertainties. Concepts of robustness and goal-oriented adaptive algorithms have therefore to be developed. Among the applications, we find the design of nuclear reactor, automotive, airplane, etc.

Lectures

* Introduction to Randomized Black-Box Numerical Optimization and CMA-ES - Anne Auger (INRIA Saclay) et Dimo Brockhoff (INRIA Saclay) - Assistants: Dimo Brockhoff (INRIA Saclay), Asma Atamna (INRIA Saclay)

This lecture focuses on difficult numerical optimization problems in black-box scenario, that is the objective function to be optimized is only known through a black-box. We additionally assume that the black-box does not return any derivatives (gradient).

After discussing the main difficulties encountered in black-box optimization, we will present some general algorithmic concepts to handle those difficulties. We will then focus on the state-of-the art method, namely the CMA-ES algorithm recognized to be one of the most efficient algorithms in complex situations. We will explain its main mechanisms for step-size and covariance matrix adaptation.

Additionally we will present some recent extension of CMA-ES for multi-objective optimization where one is interested to optimize simultaneously several conflicting objectives.

Some practical sessions will accompany the lecture. In the practical session we will teach how to use the CMA-ES algorithm in Python. At the end of the lecture and of the practical sessions you should be able to smoothly use CMA-ES to optimize your favorite application.

Ref: A. Auger and B. Doerr (eds), Theory of randomized search heuristics: Foundations and recent developments. World Scientific Publishing, 2011.

* Bayesian optimization - Julien Bect and Emmanuel Vazquez (CentraleSupélec) - Assistants : Laurent Le Brusquet (CentraleSupélec), Rémi Stroh (CentraleSupélec)

This lecture will focus on Bayesian statistical techniques, based on Gaussian process priors (in other words, kriging metamodels) and will cover the following topics: Introduction to Bayesian optimization. Gaussian process models for uncertainty quantification. Optimal Bayesian and one-step look-ahead strategies. Loss functions and sampling criteria for constrained and/or multi-objective optimization. Extension to problems with noisy outputs or environmental variables.

Refs: Santner et al. (2003), The Design and Anaysis of Computer Experiments, Springer. Forrester et al. (2008), Engineering design via surrogate modelling: a practical guide, Chichester, Wiley.

Slides

Seminars

A lot of engineering decisions are currently based on computational models in the presence of significant uncertainty. This uncertainty is generally due to the fact that the models are always imperfect and that the available data is most of the time insufficient in terms of quality and quantity. Verification and validation (V&V) approaches can therefore be seen as a general framework for accumulating evidence to support a prediction model, while incorporating the sources of uncertainty into the prediction.

Optimization (a subfield of Operations research) involves using mathematical techniques for complex decision-making. Conventionally, a real-life or academic problem is modelized thanks to decision variables with an associated domain of possible values, these variables being subject to various constraints (wether linear or non-linear). The goal lies in finding an assignment to variables that minimize the cost (or maximize the gain) of a given objective function. A global overview of the domain, ranging from algorithm complexity to mathematical model and practical methods will be given.