Bayesian Analysis Reveals the Key to Extracting Pair Potentials from Neutron Scattering Data

Learning interaction potentials from the structure factor is frequently seen as impractical due to accuracy constraints of neutron and X-ray scattering experiments. This study reexamines this historic inverse problem using Bayesian inference and probabilistic machine learning on a Mie fluid to elucidate how measurement noise impacts the accuracy of recovered potentials. To perform reliable potential reconstruction, we recommend that scattering data must have noise smaller than 0.005 up to ∼30 Å^-1 at a standard bin width 0.05 Å^-1. At uncertainties below this threshold, Mie potentials can be determined within approximately ±1.3 for the repulsive exponent, ±0.068 Å for atomic size, and ±0.024 kcal/mol in well-depth with 95% confidence. These findings highlight the potential of uniting scattering and machine learning to overcome a century-old physics problem, infer local atomic forces to serve as a vital benchmark for model validation, and enhance the accuracy of molecular simulations.