Inverse problems for stochastic neutronics

Corentin Houpert

Abstract: The aim of this work is the estimation of nuclear parameters from neutron correlation measurements. It is an inverse problem with noised observations, this is not an exception to Feynman's quote. The physics of the neutronic system provides some hunches about the behaviour of the observations, then we will be uncertain as suggested by the remark. As this viewpoint indicates, it is necessary to quantify the level of certainty: uncertainty quantification appears as a good choice.The experimental data is the list of number of neutrons detected during time intervals of same duration. A statistical analysis based on the moments of the number of detection is performed for parameter inference.Fission neutrons are produced by bunches (between 2 and 3 on average).The neutrons originating from the same fission are time correlated. Neutron source emission is a compound Poisson process. In the detections, there will be an excess of variance with respect to a Poisson process. This fact is exploited in the Feynman method. In general, due to the correlations, moments of higher order than the mean contain information about the system.Since we are looking for not only point estimates but also the full probability distribution of the parameters, we will consider Bayesian inference and Monte Carlo Markov Chain (MCMC) sampling of the a posteriori distribution. Regarding the direct calculation of the parameters, a simple model where the phase space is reduced to a single point is implemented. With this point model, the moments have analytic expressions and can be calculated efficiently and quickly.The thesis is structured as follows.First, we recall the state of the art about basics probability, neutron point model and neutron equations, uncertainty quantification and inverse problem.Then in a second part we will establish the expressions of the observations that we get from the detection times: the empirical moments of the distribution of the number of detected neutrons.Then in a third part we will study the associated inverse problem i.e. knowing the observations what are the parameters and their uncertainties. This will be done by the use of MCMC methods with the Metropolis algorithm and covariance matrix adaptation.Finally, we will conclude about the improvements provided by the thesis and what could be continued after this work.