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