Neural functional theory for inhomogeneous fluids: Fundamentals and applications

Area of Science:

• Soft Matter Physics
• Computational Chemistry
• Statistical Mechanics

Background:

• Classical density functional theory (DFT) is a powerful tool for studying inhomogeneous fluids.
• Accurate representation of the functional map between density profiles and correlation functions remains a challenge.
• Machine learning (ML) offers new avenues for developing more accurate theoretical models.

Purpose of the Study:

• To develop a hybrid classical DFT and ML scheme for determining fluid equilibrium structure and thermodynamics.
• To represent the exact functional map using a deep neural network.
• To enable accurate multiscale predictions for soft matter systems.

Main Methods:

• A hybrid scheme combining classical density functional theory with deep neural networks.
• Training neural networks on grand canonical Monte Carlo simulation data of hard sphere fluids.
• Implementing functional calculus for accessing higher-order correlation functions and free energy.
• Validating thermal Noether sum rules and performing self-consistent density profile calculations.

Main Results:

• The hybrid scheme accurately determines the equilibrium structure and thermodynamics of inhomogeneous fluids.
• Neural network-based functionals outperform state-of-the-art fundamental measure DFT.
• The method allows for macroscopic predictions with near-simulation microscopic precision.
• Demonstrated accurate self-consistent calculation of density profiles.

Conclusions:

• Machine learning of functionals is an effective tool for the multiscale description of soft matter.
• The developed hybrid scheme offers a computationally efficient and accurate alternative to traditional DFT methods.
• This approach bridges the gap between microscopic simulations and macroscopic predictions.