# Summer school CEA-EDF-INRIA 2011

# Uncertainty quantification for numerical model validation

**Location:** CEA Cadarache

**Dates:** June, 27th to July, 8th

**Secretary:** Régis Vizet (CEA/DAM)

**Scientific organizers :** Bertrand Iooss (EDF R&D) and Marc Sancandi (CEA/DAM)

**Assistants:** Géraud Blatman (EDF R&D), Claire Cannamela (CEA/DAM), Mathieu Couplet (EDF R&D), Vincent Feuillard (EADS IW), Amandine Marrel (CEA/DEN), Nadia Pérot (CEA/DEN)

# Abstract

The increase of computing power makes possible to run many complex computer simulation codes. To model physical reality, these programs need a large number of input variables and can furnish as output a huge amount of results. Such simulation results thus become difficult to analyze. In order to measure the output variability and to determine the influence of the inputs, one needs to explore the space of the input variables. However, the dimension of the input space (from 10 to thousands) makes an exhaustive exploration impossible. Moreover, the validation of the computer code remains crucial when it is used in a predictive purpose. To deal with all these problems, probabilistic and statistical tools have been recently developed by researchers in order to furnish some solutions. The goal of this summer school is to propose an introduction to these problems of uncertainty (propagation, sensitivity analysis, optimization, calibration, validation, etc.) and to explain the main mathematical techniques which allow solving them.

# Main themes

- Design of computer experiments: exploration of high dimensional input space, use of space filling designs with good sub-space projection properties, possibility of adaptive designs, and interest about robust designs. Link with the needs of High Performance Computing (HPC).
- Analysis of computer experiments: how to link, with a small number of model runs, the inputs to the outputs? Sensitivity analysis and metamodeling techniques propose some solutions. Bayesian approach is especially suitable to this purpose because it offers a systematic treatment of the uncertainties (due to small number of runs, poor uncertainty modelling, eliciting expert judgment, etc.).
- The calibration and validation steps concern the comparisons between model predictions and real observations. The goal is to give some credibility to the computer simulations. Another important issue is the computer code verification: does the computer solves correctly the model equations?

# Lectures

- François Hemez (Los Alamos National Laboratory, USA) - Introduction to the validation of computational models
- Code and calculation verification
- Designs of computer experiments
- Sampling techniques
- Test-analysis correlation
- An end-to-end engineering application

- Rui Paulo (Université Technique de Lisbonne, Portugal) - Calibration and validation of computer models: A Bayesian approach - resume
- An outline of the Bayesian approach to statistics - slides1rp.pdf
- Computer models: generalities and emulation - slides2rp.pdf
- Computer models: calibration and validation - slides3rp.pdf
- Extensions - slides4rp.pdf

- Emmanuel Vazquez (SUPELEC, France) - Rare event estimation in output of computer model - resume
- Introduction - Monte Carlo approach - Extreme value theory - part01-nup.pdf
- Structural reliability - Elicitation of probability distributions - part02-nup.pdf
- Advanced Monte Carlo methods - part03-nup.pdf
- Sequential strategies - part04-nup.pdf

# Practical works

- In Matlab - Introduction
- In R - Introduction - Space filling designs
- Demonstration of Open TURNS - Introduction
- Demonstration of URANIE - Introduction

# Seminars

- Introduction of the summer school : Bertrand Iooss (EDF R&D) & Marc Sancandi (CEA) - slides
- Introduction à la statistique : Amandine Marrel (CEA) - slides
- Management of uncertainties in engineering practice : Alberto Pasanisi (EDF R&D) - slides
- Inverse problem and calibration of parameters : Agnès de Crécy (CEA) Part 1 & Mathieu Couplet (EDF R&D) Part 2
- Optimization with uncertainties, methods from the OMD projects : Rodolphe Le Riche (EMSE) - slides
- Acounting for the variability of experimental data when calibrating mechanical constitutive models - Géraud Blatman (EDF R&D) - slides
- Basics of global sensitivity analysis : Bertrand Iooss (EDF R&D) - slides
- The validation issue in modeling and simulation : Marc Sancandi (CEA) - slides
- Polynômes de chaos : Jean-Marc Martinez (CEA) - slides
- High Performance Computing, uncertainty quantification : Christophe Prud’homme (University of Joseph Fourier) - slides
- Conclusion of the summer school : Bertrand Iooss (EDF R&D) & Marc Sancandi (CEA) - slides

# Posters

- Cross-validation of maximum likelihood estimation of hyperparameters of Gaussian process with model misspecification - page web