Surrogate functionals for machine-learned orbital-free density functional theory

Area of Science:

• Computational Chemistry
• Materials Science
• Machine Learning

Background:

• Density Functional Theory (DFT) is a cornerstone of modern computational chemistry and materials science.
• Orbital-free DFT (OF-DFT) aims to reduce computational cost by avoiding explicit electron orbital calculations.
• Existing machine-learned functionals for OF-DFT often require complex training data and computational steps.

Purpose of the Study:

• To develop novel machine-learned energy functionals for OF-DFT.
• To enable accurate prediction of ground-state densities with reduced computational overhead.
• To improve the efficiency and scalability of OF-DFT calculations.

Main Methods:

• Introduction of surrogate functionals defined by density optimization convergence.
• Development of a gradient-descent-improvement loss for guaranteed exponential density convergence.
• Implementation of an adaptive sampling scheme to focus learning on relevant optimization trajectories.
• Training and evaluation on QM9 and QMugs benchmarks.

Main Results:

• Surrogate functionals achieve density errors competitive with or superior to existing state-of-the-art methods.
• Elimination of the O(N^3) orthonormalization step, crucial for computational efficiency.
• Demonstrated improved runtime scaling for larger systems compared to prior work.
• Training requires only ground-state densities, simplifying the data acquisition process.

Conclusions:

• Surrogate functionals offer a promising new direction for efficient and accurate OF-DFT.
• The proposed training methodology simplifies data requirements and enhances convergence.
• This approach significantly improves the scalability of OF-DFT for complex systems.