Overfitting by design: neural network density functionals for water

TL;DR

This paper introduces a neural network-based exchange-correlation functional for density functional theory tailored to water, achieving high accuracy with minimal training data and enabling system-specific predictions.

Contribution

The authors develop a system-specific neural network density functional for water that improves accuracy over traditional methods and demonstrates effective transfer learning with limited data.

Findings

Achieves 1 kcal/mol error on coupled cluster energies.

Improves spectral, electron density, and geometry predictions from few configurations.

Transfer learning yields results comparable to higher-rung functionals with minimal data.

Abstract

In density functional theory, simpler exchange-correlation (XC) approximations such as the local density approximation (LDA) are favored for computational speed but rely on limited information, leading to a trade-off between accuracy and generality. Machine-learned XC approximations have seen a lot of interest to address this problem. Here, we train a neural network LDA using a differentiable Kohn-Sham solver, imparting system-specific expertise for water and sacrificing generality for accuracy. Our model achieves 1 kcal / mol errors on gold standard coupled cluster ionization and atomization energies, and improves predictions of spectral lines, electron density distribution, and equilibrium geometry from as few as eight configurations used for training. We proceed to perform transfer learning and obtain results comparable to higher-rung PBE and B3LYP functionals on the WATER27 subset of the GMTKN55 database, even when only a single two-molecule binding energy is used in the transfer process. This result opens the door for specialist functionals to be trained on different systems from little data, enhancing predictions while maintaining low training costs. Our approach of training a modified XC density functional approximation (DFA) furthermore allows for a highly interpretable result, as the neural network directly corresponds to a correction of the XC energy per electron.