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

Area of Science:

• Computational physics
• Statistical mechanics
• Materials science

Background:

• Inferring liquid structure from scattering data is crucial for understanding material properties.
• Traditional methods face numerical challenges like discrete binning and detector windowing.
• Quantifying uncertainty in radial distribution functions is essential for reliable analysis.

Purpose of the Study:

• To develop a robust nonparametric Bayesian framework for inferring radial distribution functions.
• To address numerical challenges in Fourier transforms of scattering data.
• To provide accurate uncertainty quantification for experimental structural analysis.

Main Methods:

• Utilized nonstationary Gaussian processes for a Bayesian inference framework.
• Designed Gaussian process prior mean and kernel functions to handle Fourier transform challenges.
• Implemented uncertainty propagation from the Gaussian process posterior.

Main Results:

• Successfully inferred radial distribution functions from scattering measurements.
• Demonstrated effective uncertainty quantification for the derived functions.
• Validated the method using experimental data for liquid argon and water.

Conclusions:

• The proposed Bayesian framework offers a reliable method for structural analysis of liquids.
• This approach provides a benchmark for molecular models and experimental data interpretation.
• The framework successfully integrates physical knowledge while mitigating numerical issues.