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Due to the lack of phase information, determining the physical parameters ofmultilayer thin films from measured neutron and X-ray reflectivity curves is,on a fundamental level, an underdetermined inverse problem. This so-calledphase problem poses limitations on standard neural networks, constraining therange and number of considered parameters in previous machine learningsolutions. To overcome this, we present an approach that utilizes priorknowledge to regularize the training process over larger parameter spaces. Wedemonstrate the effectiveness of our method in various scenarios, includingmultilayer structures with box model parameterization and a physics-inspiredspecial parameterization of the scattering length density profile for amultilayer structure. By leveraging the input of prior knowledge, we canimprove the training dynamics and address the underdetermined ("ill-posed")nature of the problem. In contrast to previous methods, our approach scalesfavorably when increasing the complexity of the inverse problem, workingproperly even for a 5-layer multilayer model and an N-layer periodic multilayermodel with up to 17 open parameters.

Neural network analysis of neutron and X-ray reflectivity data: Incorporating prior knowledge for tackling the phase problem