[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-956912","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Multiphysics and Uncertainties\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          2\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemester:\n          Semestre 2\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ELecture:\u003C\/span\u003E\n                                      \u003Cspan\u003E12\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003EPractical study :\u003C\/span\u003E\n                                      \u003Cspan\u003E3\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                                                          \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EMathematics: Notions of differential equations, numerical analysis, linear algebra\u003C\/p\u003E\n\u003Cp\u003EPhysics: Notions of thermal-hydraulics, neutronics, thermics. Notions of nuclear reactor operation.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EThis course is an introduction to multiphysics and to the quantification of uncertainty in the frame of nuclear reactor modeling.\u003C\/p\u003E\n\u003Cp\u003EThe couplings between the usual modeling of each of the nuclear reactor core physics domains will be recalled. The different approaches to deal with couplings will be presented, in connection with the objectives of computer simulation, in particular the nuclear safety demonstration.\u003C\/p\u003E\n\u003Cp\u003EA practical work session will allow, through the construction of a code coupling, to address the challenges related to the implementation of such calculations. The behavior of a simulated nuclear reactor core, during simple multiphysics transients, will also be observed on this occasion.\u003C\/p\u003E\n\u003Cp\u003EWe will introduce the concepts of convergence and stability, which are key for multiphysics simulations. The most used coupling algorithms and time schemes will be presented.\u003C\/p\u003E\n\u003Cp\u003EThe course will also tackle the theoretical concepts related to the treatment of uncertainties, from the description of the sources of uncertainty (probability laws, covariance, correlation), to the propagation of uncertainties and to sensitivity studies via surrogate models (neural networks, kriging).\u003C\/p\u003E\n\u003Cp\u003EFinally, we will present the recent advances in Monte Carlo codes that pave the way for multiphysics transient simulations. We will also discuss the challenges that still need to be overcome.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E- Describe the steps between the observation of a physical phenomenon and its simulation.\u003C\/p\u003E\n\u003Cp\u003E- Explain the terms used to describe multiphysics calculations (coupling, one-way coupling, partitioned, monolithic, explicit, implicit etc.).\u003C\/p\u003E\n\u003Cp\u003E- Describe the couplings between the physics involved in the usual modeling of nuclear reactor cores.\u003C\/p\u003E\n\u003Cp\u003E- Describe the main approaches used to take into account these couplings, the most used multiphysics models.\u003C\/p\u003E\n\u003Cp\u003E- Discuss these approaches and models, their use and their asset.\u003C\/p\u003E\n\u003Cp\u003E- Explain the impact of coupled calculations on the development of computer codes.\u003C\/p\u003E\n\u003Cp\u003E- Describe a simple multiphysics transient.\u003C\/p\u003E\n\u003Cp\u003E- Describe the issues of stability and precision in the development of multiphysics calculation schemes.\u003C\/p\u003E\n\u003Cp\u003E- Discuss the advantages of the most common time schemes used in multiphysics calculations.\u003C\/p\u003E\n\u003Cp\u003E- Clarify how to implement these time schemes in a code coupling.\u003C\/p\u003E\n\u003Cp\u003E- Point out the differences and advantages of the most common coupling algorithms (Gauss-Seidel, Newton, JFNK, Anderson).\u003C\/p\u003E\n\u003Cp\u003E- Spell out the nature of the uncertainties under discussion.\u003C\/p\u003E\n\u003Cp\u003E- Explain the difference between interaction and correlation (whatever its nature) between variables in order to be able to sort out what methods might be of use.\u003C\/p\u003E\n\u003Cp\u003E- Explain the basic probability concepts that describe randomness (location and dispersion parameters for instance).\u003C\/p\u003E\n\u003Cp\u003E- Describe a probability law with its basic statistical properties (mean, variance, mode\u2026) and compare one law to another one of the same kind.\u003C\/p\u003E\n\u003Cp\u003E- Spell out the concept of experimental estimators along with their underlying biases and variance terms and compute simple ones (mean, variance\u2026) when dealing with provided samples.\u003C\/p\u003E\n\u003Cp\u003E- Explain the role of the central limit theorem when computing the average of a sample and use it to estimate a rough 95% confidence interval for the sample mean.\u003C\/p\u003E\n\u003Cp\u003E- Choose a strategy to generate a design-of-experiment, when no data are available, in order to pursue the requested analysis.\u003C\/p\u003E\n\u003Cp\u003E- Explain the basic blocks of uncertainty quantification for a generic problem.\u003C\/p\u003E\n\u003Cp\u003E- Briefly detail the purpose of a sensitivity analysis and the various possible techniques that can be used, depending on the aim of the analysis.\u003C\/p\u003E\n\u003Cp\u003E- Explain the generic concept of surrogate models (from the training, quality assessment to the prediction step) and be able to mention different models.\u003C\/p\u003E\n\u003Cp\u003E- Adapt the aforementioned blocks and possibly combine them for a given problem that would take under consideration specific issues (CPU\/time consumption for a code, number of input variables...).\u003C\/p\u003E\n\u003Cp\u003E- Explain the effects of the statistical uncertainty on the results provided by a Monte Carlo code when its output is provided to another simulation code.\u003C\/p\u003E\n\u003Cp\u003E- Name et explain the variance-reduction techniques that can be used in order to reduce the statistical uncertainty.\u003C\/p\u003E\n\u003Cp\u003E- Identify\/Construe the specific issues concerning the coupling of a Monte Carlo code (as a solver for neutron transport) with external codes providing the reactivity feedbacks due to temperature and density effects, or mechanical deformations.\u003C\/p\u003E\n\u003Cp\u003E- Explain the stability of the coupling scheme: illustrate the effects of the statistical noise (induced by Monte Carlo simulations) on the transmission of the information between the codes and on the overall stability.\u003C\/p\u003E\n\u003Cp\u003E- Discuss the role of parallel simulations and the performances in terms of computation time and memory occupation.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EOrganisation g\u00e9n\u00e9rale et modalit\u00e9s p\u00e9dagogiques\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003ECourse and practical work.\u0026nbsp;Student participation is encouraged.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EComp\u00e9tences\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E- Judge of the relevance of a model of a nuclear reactor core.\u003C\/p\u003E\n\u003Cp\u003E- Identify the methods that can be used to assess the uncertainty of a simulation.\u003C\/p\u003E\n\u003Cp\u003E- Debate the issues and challenges of current R\u0026amp;D on these issues.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Continue non Int\u00e9grale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]