Description

Graph neural networks (GNN) offer a potential method of bypassing the Kohn-Sham equations in density functional theory (DFT) calculations by learning both the Hohenberg-Kohn (HK) mapping of electron density to energy, allowing for calculations of much larger atomic systems and

Graph neural networks (GNN) offer a potential method of bypassing the Kohn-Sham equations in density functional theory (DFT) calculations by learning both the Hohenberg-Kohn (HK) mapping of electron density to energy, allowing for calculations of much larger atomic systems and time scales and enabling large-scale MD simulations with DFT-level accuracy. In this work, we investigate the feasibility of GNNs to learn the HK map from the external potential approximated as Gaussians to the electron density ๐‘›(๐‘Ÿ), and the mapping from ๐‘›(๐‘Ÿ) to the energy density ๐‘’(๐‘Ÿ) using Pytorch Geometric. We develop a graph representation for densities on radial grid points and determine that a k-nearest neighbor algorithm for determining node connections is an effective approach compared to a distance cutoff model, having an average graph size of 6.31 MB and 32.0 MB for datasets with ๐‘˜ = 10 and ๐‘˜ = 50 respectively. Furthermore, we develop two GNNs in Pytorch Geometric, and demonstrate a decrease in training losses for a ๐‘›(๐‘Ÿ) to ๐‘’(๐‘Ÿ) of 8.52 ยท 10^14 and 3.10 ยท 10^14 for ๐‘˜ = 10 and ๐‘˜ = 20 datasets respectively, suggesting the model could be further trained and optimized to learn the electron density to energy functional.

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    Title
    • Improving Quantum Mechanical Calculations Using Graph Neural Networks to Predict Energies from Atomic Structure
    Contributors
    Date Created
    2023-05
    Resource Type
  • Text
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