Neural network analysis of neutron and X-ray reflectivity data:
  Incorporating prior knowledge for tackling the phase problem
Valentin Munteanu Vladimir Starostin Alessandro Greco Linus Pithan Alexander Gerlach Alexander Hinderhofer Stefan Kowarik Frank Schreiber
Due to the lack of phase information, determining the physical parameters of
multilayer thin films from measured neutron and X-ray reflectivity curves is,
on a fundamental level, an underdetermined inverse problem. This so-called
phase problem poses limitations on standard neural networks, constraining the
range and number of considered parameters in previous machine learning
solutions. To overcome this, we present an approach that utilizes prior
knowledge to regularize the training process over larger parameter spaces. We
demonstrate the effectiveness of our method in various scenarios, including
multilayer structures with box model parameterization and a physics-inspired
special parameterization of the scattering length density profile for a
multilayer structure. By leveraging the input of prior knowledge, we can
improve the training dynamics and address the underdetermined ("ill-posed")
nature of the problem. In contrast to previous methods, our approach scales
favorably when increasing the complexity of the inverse problem, working
properly even for a 5-layer multilayer model and an N-layer periodic multilayer
model with up to 17 open parameters.