Fig. 1: Schematic overview of machine-learning integration into the direct and inverse scattering problem.

a The ML workflow used here to drive the scattering experiment with automated data analysis and feeding back vital information. The workflow is split into four main sections: (I) scattering experiment design and optimization; (II) parameter space exploration and information compression; (III) structure or property predictions; and (IV) parameter space predictions. Section II links to both III and IV via latent space, \({{{{{{{\mathcal{LS}}}}}}}}\), a compressed version of the large pixel space. Dashed lines with a silhouette indicate parts of the flow that currently still require some human intervention. The latent space representations, S(L), are used in surrogates that bypass expensive calculations. b Schematic design of the surrogate model used to predict S(L) and S(Q) for a model with a given set of parameters, \({{{{{{{\mathcal{H}}}}}}}}(p)\). It comprises a radial basis network, mapping parameter space to latent space and a decoder to reconstruct S(Q) from latent space representations. The training of the surrogate is done based on a set of S(L) obtained from a set of models at different parameters, \(\{{{{{{{{\mathcal{H}}}}}}}}(p)\}\), using Monte Carlo simulations and NLAE encoding. These surrogates are used for exhaustive searches of parameter space, identifying phases and phase transitions, and predicting optimal regions for experimental study. More simulations are done iteratively in the areas of interest, and the surrogates are trained accordingly to improve their prediction accuracy.