A machine learning inversion scheme for determining interaction from scattering

Small angle scattering techniques have now been routinely used to quantitatively determine the potential of mean force in colloidal suspensions. However the numerical accuracy of data interpretation is often compounded by the approximations adopted by liquid state analytical theories. To circumvent this long standing issue, here we outline a machine learning strategy for determining the effective interaction in the condensed phases of matter using scattering. Via a case study of colloidal suspensions, we show that the effective potential can be probabilistically inferred from the scattering spectra without any restriction imposed by model assumptions. Comparisons to existing parametric approaches demonstrate the superior performance of this method in accuracy, efficiency, and applicability. This method can effectively enable quantification of interaction in highly correlated systems using scattering and diffraction experiments. Gels, foams, and paints fall into a class of soft matter materials with widespread usage in modern technologies. This paper combines machine learning and spectral analysis techniques to develop a toolbox to model the complex interactions in this family of materials, which allows to quantitatively extract the system parameters from data.