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Computerised simulations are used for designing complex systems and for optimising their performances, from a technical, an economical, or even an environmental point of view. They are now widely used in automotive industry, aeronautics, or energy production. For instance nowadays, simulation tools give access to the design and the production of business aircrafts, without any prototype development. In the energy field, simulations tend to replace expensive thermo-hydraulic tests in order to optimise the reactor use, or even to evaluate more precisely their safety factor by taking into account the ageing structures process... These computerised simulations are generally based on the evaluation of extremely complex models.

Various sources of uncertainty must be taken into account if these simulations are to be realistic : uncertainty may be due to the model, to inaccurate or partially unknown inputs or outputs, to external perturbations, aging, etc.

Therefore, it is important to develop techniques to characterise and if possible minimise the effect of these sources of uncertainty on design objectives.

In this area, Digiteo partners are very active in addressing various and complementary topics, among which one can cite :

  • Error representation, propagation and assessment, for instance via models such as Polynomial chaos, improved Monte-Carlo methods, interval calculus
  • Approximate modelling, for instance using surrogate modelling methodology, and characterisation of prediction inaccuracy, for instance via kernel based representation (e.g. Kriging)
  • Sensitivity analysis and analysis of variance, using for instance Sobol’s indices
  • Experiment design to select numerical simulations to reduce the effect of uncertainty
  • Estimation of extreme values and percentiles
  • Robust optimisation
  • Protection against outliers

All the problems above are studied in various contexts, with in mind diverse application areas.

Digiteo partners have started the organisation of a series of meetings for mutual presentations of problems and solutions in order to encourage as many cross fertilisations as possible.

Since 2005, Digiteo organises a monthly seminar titled Apprenteo, alternatively held in LRI and Supelec. It is mainly devoted to statistical learning and is also related to the subjects addressed in Section Statistical Modelling and Analysis for Stochastic Processes.

Complementarities between deterministic and statistical approaches for the characterisation of uncertainty in major calculation codes are also a research area for Digiteo. Partners within Digiteo have the, not so widely held, ability jointly to use numerical and symbolic aspects for model development.