Neural density functionals: Local learning and pair-correlation matching.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Machine Learning

Background:

• Density-Functional Theory (DFT) is a cornerstone of modern electronic structure calculations.
• Neural networks offer a promising avenue for developing novel density functionals.
• Existing methods often struggle with capturing complex correlation effects and generalizing beyond training data.

Purpose of the Study:

• To evaluate the effectiveness of bulk pair-correlation matching for training neural density functionals.
• To demonstrate the benefits of local learning of inhomogeneous one-body direct correlations.
• To advocate for local one-body learning for flexible and accurate modeling of the Mermin-Evans density-functional map.

Main Methods:

• Utilizing pair-correlation matching as proposed by Dijkman et al. for training neural functionals.
• Implementing local learning of inhomogeneous one-body direct correlations.
• Applying spatial localization techniques to neural network architectures, including convolutional neural networks.

Main Results:

• The proposed method acts as an efficient regularizer for neural density functionals.
• Local one-body learning provides a flexible framework for modeling the full Mermin-Evans density-functional map.
• Accurate neural free-energy functionals, capable of generalizing beyond the training box, were achieved.

Conclusions:

• Local learning of one-body correlations is a superior approach for developing flexible and accurate neural density functionals.
• Spatial localization is key to creating neural functionals that transcend training data limitations.
• This work advances the development of machine learning-based methods in electronic structure theory.