We present a nonparametric Bayesian framework to infer radial distribution functions from experimental scattering measurements with uncertainty quantification using nonstationary Gaussian processes. The Gaussian process prior mean and kernel functions are designed to mitigate well-known numerical challenges with the Fourier transform, including discrete measurement binning and detector windowing, while encoding fundamental yet minimal physical knowledge of the liquid structure. We demonstrate uncertainty propagation of the Gaussian process posterior to unmeasured quantities of interest. Experimental radial distribution functions of liquid argon and water with uncertainty quantification are provided as both a proof of principle for the method and a benchmark for molecular models.

Department of Chemical Engineering and Material Science University of Minnesota Twin Cities Minneapolis Minnesota 55455 United States

Department of Chemical Engineering University of Utah Salt Lake City Utah 84112 9203 United States

Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences Flemingovo nám 2 166 10 Prague 6 Czech Republic

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