Predicting Colloidal Interaction Parameters from Small Angle X-Ray Scattering Curves Using Artificial Neural Networks and Markov Chain Monte Carlo Sampling

Small Angle X-Ray Scattering (SAXS) is a characterization technique which allows for the study of colloidal interactions by fitting the structure factor of the SAXS profile for a selected model and closure relation. However, the applicability of this approach is constrained by the limited number of existing models which can be fitted analytically, as well as the narrow operating range for which the models are valid. In this work, we demonstrate a proof-of-concept for using an artificial neural network (ANN) trained on small-angle x-ray scattering (SAXS) curves obtained from Monte Carlo (MC) simulations to predict values of the effective macroion valency (Zeff) and the Debye length (κ) for a given SAXS profile. This ANN, which was trained on 200,000 simulated SAXS curves, was able to predict values of Zeff and κ for a test set containing 25,000 simulated SAXS curves with ±20% accuracy to the ground truth values. Subsequently, an ANN was used as a surrogate model in a Markov Chain Monte Carlo sampling algorithm to obtain maximum a posteriori (MAP), associated confidence intervals estimates and details of correlations of Zeff and κ for an experimentally obtained SAXS profile.