Bridging electronic and classical density-functional theory using universal machine-learned functional...

Area of Science:

• Computational Physics
• Materials Science
• Statistical Mechanics

Background:

• Density-functional theory (DFT) accuracy relies on approximations for nonlocal functionals (exchange-correlation in electronic DFT, excess in classical DFT).
• Current approximations are often semi-local or limited nonlocal forms, despite exact functionals being highly nonlocal.
• Machine learning (ML) offers potential for improved nonlocal functional approximations in both electronic and classical DFT.

Purpose of the Study:

• To develop a universal machine-learning framework for learning nonlocal density-functional approximations.
• To unify disparate ML approaches used in electronic and classical DFT research.
• To create accurate nonlocal functionals applicable across a diverse range of systems.

Main Methods:

• Formulation of a universal ML framework combining equivariant convolutional neural networks and the weighted-density approximation.
• Development of a standardized training protocol for learning nonlocal functionals.
• Prototyping and testing the framework on 1D and quasi-1D systems.

Main Results:

• Demonstrated excellent accuracy for a diverse set of systems using identical hyperparameters.
• Successfully applied the ML functionals to hard-rod fluids, inhomogeneous Ising models, and electron exchange energy.
• Achieved accurate results for electron kinetic energy in orbital-free DFT and liquid water with 1D inhomogeneities.

Conclusions:

• The developed universal ML framework provides a generalized approach to learning nonlocal functionals.
• This unified method shows significant promise for approximating exact 3D functionals in both electronic and classical DFT.
• Establishes a foundation for advancing DFT applications across multiple scientific domains.