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Computer experiments & Waves propagation

Presentation

Program (detailed content) :

 

Computer Experiments

  • 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

 

Waves

  • Main models of wave propagation: acoustic waves, wave equation, Schrödinger equations.
  • Boundary conditions: physical boundaries, artificial boundary (transparent, absorbing boundary conditions, perfectly matched layers).

 

Organization :

  • Course, exercises, computer lab with R software.

Objectives

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

 

Computer Experiment

  • 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

 

Waves

  • The principle of transparent and absorbing boundary conditions for wave propagation
  • Two methods of uncertainty quantifications: chaos polynomial expansion and multi-level Monte Carlo methods

 

 

The student should be able :

 

Computer Experiments

  • 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

Waves

  • Design theoretically and numerically transparent and absorbing boundary conditions.
  • Perform numerically a UQ analysis based on intrusive methods (chaos polynomial methods) or non intrusive (multi-level Monte Carlo methods).

Needed prerequisite

Gaussian vectors. Basics of PDE: methods of characteristics, finite difference methods for PDEs.

Recommended prerequisite

Waves

Basics of PDE: methods of characteristics, finite difference methods for PDEs.

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

  • 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