Machine learning-accelerated small-angle X-ray scattering analysis of disordered two- and three-phase materials

Small-angle X-ray scattering (SAXS) is a useful technique for nanoscale structural characterization of materials. In SAXS, structural and spatial information is indirectly obtained from the scattering intensity in the spectral domain, known as the reciprocal space. Therefore, characterizing the structure requires solving the inverse problem of finding a plausible structure model that corresponds to the measured scattering intensity. Both the choice of structure model and the computational workload of parameter estimation are bottlenecks in this process. In this work, we develop a framework for analysis of SAXS data from disordered materials. The materials are modeled using Gaussian Random Fields (GRFs). We study the case of two phases, pore and solid, and three phases, where a third phase is added at the interface between the two other phases. Further, we develop very fast GPU-accelerated, Fourier transform-based numerical methods for both structure generation and SAXS simulation. We demonstrate that length scales and volume fractions can be predicted with good accuracy using our machine learning-based framework. The parameter prediction executes virtually instantaneously and hence the computational burden of conventional model fitting can be avoided.