Predicting Colloidal\nInteraction Parameters from Small-Angle\nX‑ray Scattering Curves Using Artificial Neural Networks and\nMarkov Chain Monte Carlo Sampling

Small-angle X-ray scattering (SAXS) is a characterization\ntechnique\nthat allows for the study of colloidal interactions by fitting the\nstructure factor of the SAXS profile with a selected model and closure\nrelation. However, the applicability of this approach is constrained\nby the limited number of existing models that can be fitted analytically,\nas well as the narrow operating range for which the models are valid.\nIn this work, we demonstrate a proof of concept for using an artificial\nneural network (ANN) trained on SAXS curves obtained from Monte Carlo\n(MC) simulations to predict values of the effective macroion valency\n(<i>Z</i><sub>eff</sub>) and the Debye length (κ<sup>–1</sup>) for a given SAXS profile. This ANN, which was trained\non 200,000 simulated SAXS curves, was able to predict values of <i>Z</i><sub>eff</sub> and κ<sup>–1</sup> for a test\nset containing 25,000 simulated SAXS curves, where most predicted\nvalues had errors smaller than 20%. Subsequently, an ANN was used\nas a surrogate model in a Markov chain Monte Carlo sampling algorithm\nto obtain maximum a posteriori estimates of <i>Z</i><sub>eff</sub> and κ<sup>–1</sup>, as well as the associated\nconfidence intervals and correlations between <i>Z</i><sub>eff</sub> and κ<sup>–1</sup> for an experimentally obtained\nSAXS profile.