Learned free-energy functionals from pair-correlation matching for dynamical density functional theory

Area of Science:

• Statistical mechanics
• Computational physics
• Colloidal science

Background:

• Classical density functional theory (cDFT) and dynamical density functional theory (DDFT) model many-body colloidal systems.
• Accurate excess free-energy functionals are crucial but often infeasible.
• Prior work showed neural excess free-energy functionals can be learned for cDFT.

Purpose of the Study:

• To apply a pre-learned neural excess free-energy functional to DDFT without retraining.
• To simulate nonequilibrium overdamped dynamics of inhomogeneous densities using DDFT.
• To develop and apply a gradient flow extension of DDFT for grand-canonical systems.

Main Methods:

• Utilized a neural excess free-energy functional learned via pair-correlation matching.
• Simulated three-dimensional Lennard-Jones systems with planar geometry under external potentials.
• Extended DDFT using gradient flows for grand-canonical simulations.

Main Results:

• Demonstrated successful application of the learned functional in DDFT for simulating dynamics.
• Achieved good agreement between DDFT and Brownian dynamics simulations for inhomogeneous densities.
• Showcased accurate simulations for gas adsorption systems using the extended DDFT.

Conclusions:

• A learned free-energy functional can be effectively transferred to DDFT, eliminating the need for retraining.
• This approach enables accurate and efficient modeling of complex many-body nonequilibrium systems.
• The method shows promise for applications in areas like gas adsorption studies.