Classification of grazing-incidence small-angle X-ray scattering patterns by convolutional neural network

Machine learning for analysis of experimental scattering and spectroscopy data in materials chemistry

The rapid growth of materials chemistry data, driven by advancements in large-scale radiation facilities as well as laboratory instruments, has outpaced conventional data analysis and modelling methods, which can require enormous manual effort. To address this bottleneck, we investigate the application of supervised and unsupervised machine learning (ML) techniques for scattering and spectroscopy data analysis in materials chemistry research. Our perspective focuses on ML applications in powder diffraction (PD), pair distribution function (PDF), small-angle scattering (SAS), inelastic neutron scattering (INS), and X-ray absorption spectroscopy (XAS) data, but the lessons that we learn are generally applicable across materials chemistry. We review the ability of ML to identify physical and structural models and extract information efficiently and accurately from experimental data. Furthermore, we discuss the challenges associated with supervised ML and highlight how unsupervised ML can mitigate these limitations, thus enhancing experimental materials chemistry data analysis. Our perspective emphasises the transformative potential of ML in materials chemistry characterisation and identifies promising directions for future applications. The perspective aims to guide newcomers to ML-based experimental data analysis.

Strategy to simulate and fit 2D grazing-incidence small-angle X-ray scattering patterns of nanostructured thin films

Grazing-incidence small-angle X-ray scattering (GISAXS) is a widely used method for the characterization of the nanostructure of supported thin films and enables time-resolved in situ measurements. The 2D scattering patterns contain detailed information about the nanostructures within the film and at its surface. However, this information is distorted not only by the reflection of the X-ray beam at the substrate-film interface and its refraction at the film surface but also by scattering of the substrate, the sample holder and other types of parasitic background scattering. In this work, a new, efficient strategy to simulate and fit 2D GISAXS patterns that explicitly includes these effects is introduced and demonstrated for (i) a model case nanostructured thin film on a substrate and (ii) experimental data from a microphase-separated block copolymer thin film. To make the protocol efficient, characteristic linecuts through the 2D GISAXS patterns, where the different contributions dominate, are analysed. The contributions of the substrate and the parasitic background scattering - which ideally are measured separately - are determined first and are used in the analysis of the 2D GISAXS patterns of the nanostructured, supported film. The nanostructures at the film surface and within the film are added step by step to the real-space model of the simulation, and their structural parameters are determined by minimizing the difference between simulated and experimental scattering patterns in the selected linecuts. Although in the present work the strategy is adapted for and tested with BornAgain, it can be easily used with other types of simulation software. The strategy is also applicable to grazing-incidence small-angle neutron scattering.

Machine learning for scattering data: strategies, perspectives and applications to surface scattering

Machine learning (ML) has received enormous attention in science and beyond. Discussed here are the status, opportunities, challenges and limitations of ML as applied to X-ray and neutron scattering techniques, with an emphasis on surface scattering. Typical strategies are outlined, as well as possible pitfalls. Applications to reflectometry and grazing-incidence scattering are critically discussed. Comment is also given on the availability of training and test data for ML applications, such as neural networks, and a large reflectivity data set is provided as reference data for the community.

Parameter inversion of a polydisperse system in small-angle scattering

An accurate and efficient method for model- and form-free inversion of a polydisperse small-angle scattering system is presented. It supports an arbitrary number of model parameters and both 1D and 2D intensity observations.

A general method to invert parameter distributions of a polydisperse system using data acquired from a small-angle scattering (SAS) experiment is presented. The forward problem, i.e. calculating the scattering intensity given the distributions of any causal parameters of a theoretical model, is generalized as a multi-linear map, characterized by a high-dimensional Green tensor that represents the complete scattering physics. The inverse problem, i.e. finding the maximum-likelihood estimation of the parameter distributions (in free form) given the scattering intensity (either a curve or an image) acquired from an experiment, is formulated as a constrained nonlinear programming (NLP) problem. This NLP problem is solved with high accuracy and efficiency via several theoretical and computational enhancements, such as an automatic data scaling for accuracy preservation and GPU acceleration for large-scale multi-parameter systems. Six numerical examples are presented, including both synthetic tests and solutions to real neutron and X-ray data sets, where the method is compared with several existing methods in terms of their generality, accuracy and computational cost. These examples show that SAS inversion is subject to a high degree of non-uniqueness of solution or structural ambiguity. With an ultra-high accuracy, the method can yield a series of near-optimal solutions that fit data to different acceptable levels.

Neural network analysis of neutron and x-ray reflectivity data: pathological cases, performance and perspectives

Neutron and x-ray reflectometry (NR and XRR) are powerful techniques to investigate the structural, morphological and even magnetic properties of solid and liquid thin films. While neutrons and x-rays behave similarly in many ways and can be described by the same general theory, they fundamentally differ in certain specific aspects. These aspects can be exploited to investigate different properties of a system, depending on which particular questions need to be answered. Having demonstrated the general applicability of neural networks to analyze XRR and NR data before (Greco et al 2019 J. Appl. Cryst. 52 1342), this study discusses challenges arising from certain pathological cases as well as performance issues and perspectives. These cases include a low signal-to-noise ratio, a high background signal (e.g. from incoherent scattering), as well as a potential lack of a total reflection edge (TRE). By dynamically modifying the training data after every mini batch, a fully-connected neural network was trained to determine thin film parameters from reflectivity curves. We show that noise and background intensity pose no significant problem as long as they do not affect the TRE. However, for curves without strong features the prediction accuracy is diminished. Furthermore, we compare the prediction accuracy for different scattering length density combinations. The results are demonstrated using simulated data of a single-layer system while also discussing challenges for multi-component systems.

Probabilistic parameter estimation using a Gaussian mixture density network: application to X-ray reflectivity data curve fitting

X-ray reflectivity (XRR) is widely used for thin-film structure analysis, and XRR data analysis involves minimizing the difference between experimental data and an XRR curve calculated from model parameters describing the thin-film structure. This analysis takes a certain amount of time because it involves many unavoidable iterations. However, the recently introduced artificial neural network (ANN) method can dramatically reduce the analysis time in the case of repeated analyses of similar samples. Here, the analysis of XRR data using a mixture density network (MDN) is demonstrated, which enables probabilistic prediction while maintaining the advantages of an ANN. First, under the assumption of a unimodal probability distribution of the output parameter, the trained MDN can estimate the best-fit parameter and, at the same time, estimate the confidence interval (CI) corresponding to the error bar of the best-fit parameter. The CI obtained in this manner is similar to that obtained using the Neumann process, a well known statistical method. Next, the MDN method provides several possible solutions for each parameter in the case of a multimodal distribution of the output parameters. An unsupervised machine learning method is used to cluster possible parameter sets in order of probability. Determining the true value by examining the candidates of the parameter sets obtained in this manner can help solve the inherent inverse problem associated with scattering data.