Neural network analysis of neutron and X-ray reflectivity data: Incorporating prior knowledge for tackling the phase problem
This addresses an underdetermined inverse problem in materials science, offering a scalable solution for analyzing complex multilayer structures.
The paper tackled the phase problem in determining physical parameters of multilayer thin films from neutron and X-ray reflectivity data by incorporating prior knowledge to regularize neural network training, enabling effective scaling to models with up to 17 parameters.
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.