  Grazing incidence X-ray fluorescence is a non-destructive technique for
analyzing the geometry and compositional parameters of nanostructures appearing
e.g. in computer chips. In this paper, we propose to reconstruct the posterior
parameter distribution given a noisy measurement generated by the forward model
by an appropriately learned invertible neural network. This network resembles
the transport map from a reference distribution to the posterior. We
demonstrate by numerical comparisons that our method can compete with
established Markov Chain Monte Carlo approaches, while being more efficient and
flexible in applications.
