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

TL;DR

This paper introduces a Bayesian Gaussian process framework for inferring liquid structure from scattering data, effectively handling measurement challenges and providing uncertainty quantification for radial distribution functions.

Contribution

It develops a physics-informed nonparametric Bayesian approach that mitigates Fourier transform issues and encodes physical knowledge, advancing liquid structure inference from scattering data.

Findings

Successfully infers radial distribution functions of liquids with uncertainty quantification.

Provides benchmark data for liquid argon and water.

Implementation available on GitHub for reproducibility.

Abstract

We present a nonparametric Bayesian framework to infer radial distribution functions from experimental scattering measurements with uncertainty quantification using non-stationary 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 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. The full implementation is available on GitHub at: https://github.com/hoepfnergroup/LiquidStructureGP-Sullivan.