Physics-Informed Gaussian Process Inference of Liquid Structure from Scattering Data

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.