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

Area of Science:

• Computational Physics
• Materials Science
• Statistical Mechanics

Background:

• Inferring interatomic potentials from scattering data is challenging due to experimental accuracy limitations.
• Historic inverse problems in physics often face significant hurdles with traditional methods.

Purpose of the Study:

• To reexamine the inverse problem of learning interaction potentials from structure factor data.
• To investigate the impact of measurement noise on potential reconstruction accuracy using machine learning.
• To establish criteria for reliable potential recovery from scattering experiments.

Main Methods:

• Utilized Bayesian inference and probabilistic machine learning techniques.
• Applied methods to a Mie fluid model system.
• Analyzed the influence of varying levels of measurement noise on recovered potentials.

Main Results:

• Scattering data noise must be below 0.005 up to ~30 Å⁻¹ (bin width 0.05 Å⁻¹) for reliable potential reconstruction.
• Mie potentials determined with high confidence (95%) within ±1.3 for repulsive exponent, ±0.068 Å for atomic size, and ±0.024 kcal/mol for well-depth.
• Demonstrated the feasibility of accurate potential recovery under specific noise conditions.

Conclusions:

• Uniting scattering experiments with machine learning offers a powerful approach to solve inverse problems in physics.
• Provides a method to infer local atomic forces, crucial for validating simulation models.
• Enhances the accuracy and reliability of molecular simulations by providing accurate interaction potentials.