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)
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.
* 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.
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- TP: Introudction to python
- TP: Exercise
- TP solution (you have to suppress the .pdf extension after downloading)
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.
- Basics of VV&UQ - Guillaume Perrin (CEA/DAM) - slides
- Basics of optimization methods - Jean-Yves Lucas (EDF R&D) - slides
- Lectures on applications
- Jean-Marc Martinez (CEA/DEN) : Zonage du coeur Astrid
- Jean-Yves Lucas (EDF R&D) : Optimisation du paramétrage d’une chaudière charbon Q600 - slides
- Philippe Mellinger (CEA/DAM) : Optimisation bayésienne multi-objectif d’une expérience laser