  In a fissile material, the inherent multiplicity of neutrons born through
induced fissions leads to correlations in their detection statistics. The
correlations between neutrons can be used to trace back some characteristics of
the fissile material. This technique known as neutron noise analysis has
applications in nuclear safeguards or waste identification. It provides a
non-destructive examination method for an unknown fissile material. This is an
example of an inverse problem where the cause is inferred from observations of
the consequences. However, neutron correlation measurements are often noisy
because of the stochastic nature of the underlying processes. This makes the
resolution of the inverse problem more complex since the measurements are
strongly dependent on the material characteristics. A minor change in the
material properties can lead to very different outputs. Such an inverse problem
is said to be ill-posed. For an ill-posed inverse problem the inverse
uncertainty quantification is crucial. Indeed, seemingly low noise in the data
can lead to strong uncertainties in the estimation of the material properties.
Moreover, the analytical framework commonly used to describe neutron
correlations relies on strong physical assumptions and is thus inherently
biased. This paper addresses dual goals. Firstly, surrogate models are used to
improve neutron correlations predictions and quantify the errors on those
predictions. Then, the inverse uncertainty quantification is performed to
include the impact of measurement error alongside the residual model bias.
