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Computer experiments & Experimental Design

Presentation

Program (detailed content) :

 

Experimental Design Part :

  • Linear covariance models, multiple interactions, mixed models.
  • Principle of randomized experiments and classical experiments design
  • Factorial, fractional designs
  • Examples with the SAS or JMP software

 

Computer Experiment Part :

  • Introduction: computer experiments and metamodelling. Examples of applications
  • Two famous metamodels : chaos polynomials and Gaussian process regression (Kriging)
  • Simulation of unconditional / conditional Gaussian processes
  • Accounting for external knowledge and covariance kernel customization
  • Metamodel-based optimisation (Bayesian optimisation)
  • Design of computer experiments: focus on space-filling design
  • Global sensitivity analysis: focus on ANOVA decomposition (Sobol decomposition)
  • Industrial application: uncertainty quantification

 

Organization :

  • Course, exercises, computer lab with R and JMP  softwares.

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts) :

  • The main methods of experimental design
  • Metamodelling for optimization / uncertainty quantification of a computer code
  • At least the two main families of metamodels : chaos polynomials and Gaussian processes
  • Kernel customization to account for external knowledge
  • Design of computer experiments
  • Global sensivity analysis

 

The student should be able :

 

Experimental Design part :

  • Plan an experiment in the framework of a linear model

 

Computer Experiment part :

  • At a theoretical level, to do computations for:
    • covariance kernels and Gaussian process
    • ANOVA decomposition, Sobol indices
  • At a practical level, to perform the complete methodology for analyzing a computer code
    • design of experiments
    • metamodel construction / evaluation
    • application to optimization / uncertainty quantification of a computer code

Needed prerequisite

  • Elements of statistical modelling [I4MMMS71]
  • Softwares and methods of statistical exploratory data analysis [4MMSP81]
  • Gaussian vectors.

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...

Bibliography

  • Azais, J.M. et Bardet, J.M. (2005)
  • Le modèle linéaire par l'exemple, Dunod.
  • Gaussian process for machine learning, C. E. Rasmussen and C. K. I. Williams, The MIT Press, 2006.

http://www.gaussianprocess.org/gpml/

  • B. Iooss. Revue sur l'analyse de sensibilité globale de modèles numériques. Journal de la Société Française de Statistique, 152:1-23, 2011

http://journal-sfds.fr/article/view/53