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

TL;DR

This paper introduces a neural network method that incorporates prior knowledge to effectively solve the phase problem in neutron and X-ray reflectivity data analysis, enabling accurate modeling of complex multilayer structures.

Contribution

The authors develop a regularization approach using prior knowledge to expand neural network capabilities for complex multilayer reflectivity inverse problems.

Findings

Improved neural network training with prior knowledge regularization.

Successful modeling of multilayer structures with up to 17 parameters.

Scalable approach for complex multilayer inverse problems.

Abstract

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.