Learning Neural Free-Energy Functionals with Pair-Correlation Matching.

Area of Science:

• Computational physics
• Statistical mechanics
• Materials science

Background:

• Classical density functional theory relies on the intrinsic Helmholtz free-energy functional, which is often approximated for 3D systems.
• Accurate free-energy functionals are essential for predicting material properties and phase behavior.

Purpose of the Study:

• To develop a novel method for learning an accurate neural-network approximation of the Helmholtz free-energy functional.
• To circumvent the need for computationally expensive sampling of heterogeneous density profiles.

Main Methods:

• A neural network was trained exclusively on a dataset of radial distribution functions.
• The method was applied to a supercritical Lennard-Jones system with planar symmetry.

Main Results:

• The learned neural free-energy functional accurately predicted inhomogeneous density profiles.
• Predictions were validated under various complex external potentials derived from simulations.

Conclusions:

• This data-driven approach offers a computationally efficient alternative for approximating free-energy functionals.
• The method shows promise for advancing classical density functional theory applications in complex systems.