Embedding material graphs using the electron-ion potential: application to material fracture

At the heart of the flourishing field of machine learning potentials are graph neural networks, where deep learning is interwoven with physics-informed machine learning (PIML) architectures. Various PIML models, upon training with density functional theory (DFT) material structure-property datasets, have achieved unprecedented prediction accuracy for a range of molecular and material properties. A critical component in the learned graph representation of crystal structures in PIMLs is how the various fragments of the structure's graph are embedded in a neural network. Several of the state-of-art PIML models apply spherical harmonic functions. Such functions are based on the assumption that DFT computes the Coulomb potential of atom-atom interactions. However, DFT does not directly compute such potentials, but integrates the electron-atom potentials. We introduce the direct integration of the external potential (DIEP) methods which more faithfully reflects that actual computational workflow in DFT. DIEP integrates the external (electron-atom) potential and uses these quantities to embed the structure graph into a deep learning model. We demonstrate the enhanced accuracy of the DIEP model in predicting the energies of pristine and defective materials. By training DIEP to predict the potential energy surface, we show the ability of the model in predicting the onset of fracture of pristine and defective carbon nanotubes.