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Fundamentals of Uncertainty Quantification

Numerical simulations have reached a great maturity that allows to accurately predict physics. However, uncertainties in the model inputs limit the capacities of deterministic simulations. Uncertainty Quantification provides tools for propagating uncertainties through numerical simulators, quantifying the induced simulator output variability, ranking the inputs by their degree of significance or even analysing a risk. This course will guide you through the uncertainty world and in the end you will be able to solve some uncertainty quantification problems.

Next sessions

This training is open on request. Please contact us if you want to get the access.

Price: students : 300 € – Cerfacs shareholders : 360 € – others : 504 € (TTC)


Numerical simulations have reached a great maturity that allows to accurately predict physics. However, uncertainties in the model inputs limit the capacities of deterministic simulations. Stochastic approaches allow to overcome this limit. Uncertainty Quantification (UQ) provides tools for propagating uncertainties through numerical simulators from inputs to output, quantifying the induced simulator output variability, screening the non-significant inputs, ranking the significant ones or even estimating an exceedance probability.

Scientific content

This online training course presents the fundamental concepts of uncertainty quantification. The course content is divided in 3 consecutive weeks:

  • week 1: introduction to uncertainty quantification
  • week 2: uncertainty propagation and sensitivity analysis
  • week 3: formulation, validation and application of surrogate models

An interactive live conference will close the 3-week session, focussing on an Uncertainty Quantification analysis for an applicative test case in Computational Fluid Dynamics. The time slot for this conference will be decided regarding the attendees’ availability in week 4.

Learning outcomes

At the end of this training, you will be able to:

  • give a grounded opinion about various tools of UQ: sensitivty analysis, design of experiments, surrogate model,
  • set up a UQ analysis on a simple problem: choose an appropriate set of tools for your case study,
  • make the most of a UQ study (modelling the input uncertainties, sampling the uncertain input domain, quantifying the output uncertainty, analysing the output sensitivity with respect to the inputs…)


This is a fully online training session. It is divided into 5 consecutive weeks, based on learning activities delivered each week.

  • Week 1 to week 3 require around 2 hours of work per week. Learning activities are released on Monday of each week and you have 7 days to complete each week's activities. The 2 hours of work can be distributed over the week, depending on your schedule.
  • A 1 hour live interactive session will hold during week 4. This live session will deal with an applicative case. This live session will also be recorded.
  • Last week is dedicated to revising and a final exam, leading to a certificate of learning.

Our pedagogical principles

All our learning sessions are built upon evidence-based principles from cognitive psychology and learning research:

  • concepts first: the course is focused on conceptual understanding of the meaning of equations and how they apply in practical cases (Van Heuvelen, 1991).
  • active learning: the course is organized around activities especially designed to make participants interact between each other, involving a deep processing of the scientific content previously shown in short videos (Salmon, 2013).
  • long-term retention and transfer: because you need to apply what you will learn during this session in the future and in various contexts, our courses are designed using the 10 laboratory-tested principles drawn from cognitive psychology (Halpern and Hakel, 2003).

Be prepared to be engaged and to interact with a community sharing a common goal: learning the scientific content of this course.


While this course is not focused on mathematical aspects, a background in mathematical analysis and statistics is needed.

Course Staff

This course is designed by a group composed of expert researchers from the field supervised by an expert researcher in active online learning.

Dr. Paul Mycek

Paul Mycek received a Ph.D. in computational fluid dynamics on the numerical modelling of tidal turbines from Université du Havre (France) in 2013. After a three-year postdoc at Duke University (Durham, NC, USA), he is now working on uncertainty quantification and high performance computing at CERFACS.

Dr. Matthias De Lozzo

Matthias De Lozzo is a researcher in data science. He received a Ph.D in applied statistics on the thermal numerical modelling of an aeronautic component from Université de Toulouse (France) in 2013. After a two-year postdoc at CEA Cadarache (France) on risk management for nuclear plants, he is now working on uncertainty quantification for geosciences at CERFACS.

Dr. Jean-Christophe Jouhaud

J-C Jouhaud is a researcher at Cerfacs which has obtained the Hability to Conduct Research in 2008. His field of expertise is LES simulations, Aerothermics Coupling, Aeroacoustics and Surrogate Models (Kriging and POD).

Eng. Pamphile Roy

After a master degree in Aeronautics and Aerospace at IPSA, Pamphile Roy went to ISAE-SUPAERO to conduce an advance master in Aeronautics and Aerospace propulsion. Now he performs a PhD thesis on Uncertainty Quantification applied to blade design in a Large Eddy Simulation context. The objective to reduce the number of simulations needed.

Eng. Romain Dupuis

Romain Dupuis received his engineering degree in Energy, Fluid and Thermal Power from Mines Nancy (France) and Cranfield University (United Kingdom) in 2014. He started his Ph.D. thesis in 2015, funded by the French Institute of Technology IRT Saint-Exupery, in the context of the MDA-MDO project. His topic focuses on surrogate models applied to aerodynamics and aerothermal coupling.

Dr. J-F. Parmentier

After getting his PhD in Fluid Mechanics working on modeling of two-phase gas-particle flows, he worked for a few years on thermo-acoustic instabilities in annular combustion chambers. Since 2014 he has oriented his research specifically on learning and teaching science using active learning methods.








🎓 Soutenance de Thèse : Thibault GIOUD

Lundi 27 mai 2024Du 14h00 à 18h00

  Thèses Cerfacs       Cerfacs, Toulouse, France    





JOURNÉE des DOCTORANTS du Cerfacs (JDD2024@Cerfacs) : 30/05/2024

Jeudi 30 mai 2024Du 9h00 à 17h00

  Journée des Doctorants       CERFACS     





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