Metadensity Functional Learning for Classical Fluids: Regularizing with Pair Correlations.

Area of Science:

• Computational physics
• Soft matter physics
• Statistical mechanics

Background:

• Neural metadensity functional theory (NMFT) offers a new framework for physics.
• Understanding inhomogeneous fluids is crucial for soft matter design.
• Traditional methods like Henderson inversion can be computationally intensive.

Purpose of the Study:

• To investigate and exploit NMFT for describing inhomogeneous fluids.
• To develop "metadirect" routes for determining bulk fluid pair correlation structure.
• To explore the on-the-fly modification of pair potentials in soft matter design.

Main Methods:

• Utilizing classical density functional theory for functional relationships.
• Implementing variational calculus via neural functional line integration and automatic differentiation.
• Regularizing local learning of neural functionals by comparing different computational routes.

Main Results:

• Demonstrated efficient "metadirect" access to pair correlation structure in 1D systems.
• Matched results from metadirect functional differentiation with accurate test particle data.
• Showcased the ability to alter pair potentials during the prediction stage.

Conclusions:

• NMFT provides a first-principles approach to accessing pair structure, circumventing Ornstein-Zernike inversion.
• The developed methods are efficient for soft matter design and physics simulations.
• This work opens new avenues for computational modeling in fluid physics.