Learning to Approximate Density Functionals.

Area of Science:

• Computational chemistry and materials science
• Application of machine learning in scientific research

Background:

• Density functional theory (DFT) is widely used but limited by exchange-correlation (XC) approximations.
• Human-developed XC approximations often exceed the chemical accuracy limit.
• Machine learning (ML) offers potential to improve DFT accuracy and efficiency.

Purpose of the Study:

• To investigate the capability of ML in developing accurate density functional approximations.
• To explore ML methods for improving electronic structure calculations.
• To address the challenge of generalization for ML-derived functionals.

Main Methods:

• Kernel ridge regression for orbital-free DFT calculations.
• Training ML models on ab initio data to bypass explicit XC functional derivation.
• Utilizing deep neural networks with differentiable programming and Kohn-Sham equations as regularizers.

Main Results:

• ML successfully modeled kinetic energy and achieved chemical accuracy in molecular dynamics.
• ML-designed functionals demonstrated higher accuracy than human-designed ones, including for strongly correlated materials.
• ML-derived functionals show potential for enhanced accuracy without increased computational cost.

Conclusions:

• ML can generate superior density functional approximations compared to human design.
• ML methods are effective in handling complex electronic structure problems like strong correlation.
• Generalization of ML-derived functionals across various systems is the primary obstacle to widespread adoption.