Bridge function as a functional of the radial distribution function: Operator learning and application.

Area of Science:

• Computational physics
• Statistical mechanics
• Machine learning applications

Background:

• Integral equation theories, like the Ornstein-Zernike equation, are crucial for calculating molecular system properties.
• The hypernetted chain (HNC) approximation, a common closure relation, neglects the bridge function, limiting its accuracy.

Purpose of the Study:

• To develop a machine learning approach to predict the bridge function.
• To improve the accuracy of integral equation theories by incorporating a neural network-predicted bridge function.

Main Methods:

• A deep operator network was trained using bridge functions from Monte Carlo simulations of the Lennard-Jones fluid.
• The trained network predicts bridge functions based on the radial distribution function.
• The improved HNC closure, including the predicted bridge function, was solved iteratively.

Main Results:

• The neural network-based bridge function significantly improved predictions for the radial distribution function and pressure compared to standard HNC.
• The method demonstrated universality, showing good agreement for Mie and hard-sphere fluids using a model trained on Lennard-Jones data.

Conclusions:

• Machine learning offers a powerful tool to enhance integral equation theories in molecular simulations.
• The proposed method provides a more accurate and versatile approach to studying classical molecular systems.