Uncertainty in computer simulations, deterministic and probabilistic methods for quantifying uncertainty, OpenTurns software, Uranie software

**Content**

Uncertainty quantification takes into account the fact that most inputs to a simulation code are only known imperfectly. It seeks to translate this uncertainty of the data to improve the results of the simulation. This training will introduce the main methods and techniques by which this uncertainty propagation can be handled without resorting to an exhaustive exploration of the data space. HPC plays an important role in the subject, as it provides the computing power made necessary by the large number of simulations needed.

The course will present the most important theoretical tools for probability and statistical analysis, and will illustrate the concepts using the OpenTurns software.

**Course Outline**

**Day 1 : Methodology of Uncertainty Treatment – Basics of Probability and Statistics**

• General Uncertainty Methodology (30’) : A. Dutfoy

• Probability and Statistics: Basics (45’) : G. Blondet

• General introduction to Open TURNS and Uranie (2 * 30’) : G. Blondet, J.B. Blanchard

• Introduction to Python and Jupyter (45’): practical work on distributions manipulations

Lunch

• Uncertainty Quantification (45’) : J.B. Blanchard

• OpenTURNS – Uranie practical works: sections 1, 2 (1h): G. Blondet, J.B. Blanchard, A. Dutfoy

• Central tendency and Sensitivity analysis (1h): A. Dutfoy

**Day 2 : Quantification, Propagation and Ranking of Uncertainties**

• Application to OpenTURNS and Uranie (1h): section 3 M. Baudin, G. Blondet, F. Gaudier, J.B. Blanchard

• Estimation of probability of rare events (1h): G. Blondet

• Application to OpenTURNS and Uranie (1h): M. Baudin, G. Blondet, F. Gaudier, J.B. Blanchard

Lunch

• Distributed computing (1h) : Uranie (15’, F. Gaudier, J.B. Blanchard), OpenTURNS (15’, G. Blondet), Salome et OpenTURNS (30’, O. Mircescu)

• Optimisation and Calibration (1h) : J.B. Blanchard, M. Baudin

• Application to OpenTURNS and Uranie (1h): J.B. Blanchard, M. Baudin

**Day 3 : HPC aspects – Meta model**

• HPC aspects specific to the Uncertainty treatment (1h) : K. Delamotte

• Introduction to Meta models (validation, over-fitting) – Polynomial chaos expansion (1h) : JB Blanchard, C. Mai,

• Kriging meta model (1h): C. Mai

Lunch

• Application to OpenTURNS and Uranie (2h) : C. Mai, G. Blondet, J.B. Blanchard

• Discussion / Participants projects

**Learning outcomes**

Learn to recognize when uncertainty quantification can bring new insight to simulations.

Know the main tools and techniques to investigate uncertainty propagation.

Gain familiarity with modern tools for actually carrying out the computations in a HPC context.

**Prerequisites**

Basic knowledge of probability will be useful, as will a basic familiarity with Linux.

Link toward the registration page