npj Computational Materials - Predicting electronic structures at any length scale with machine learning
, slight deviations between the radial distribution functions of different system sizes can be seen, most notably for the cells containing a stacking fault. Overall, these deviations are small in magnitude, especially for the unperturbed cells, and generally, all radial distribution functions agree very well up to the cutoff radius from which information is incorporated into the bispectrum descriptors.
This analysis hence provides evidence that training, inference test, and the ultra-large simulation cells possess, on average, the same local environments. It indicates that our MALA predictions of the electronic structure and energy are based on interpolations on observed data. Therefore our models can be expected to be accurate at ultra-large scales far exceeding those for which reference data exists.
At system sizes where DFT benchmarks are still available, we demonstrate that our ML model is capable of reproducing energies and electronic densities of extended systems at virtually no loss in accuracy while outperforming other ML models that are based solely on energy. Furthermore, we demonstrate that our ML workflow enables predicting the electronic structure for systems with more than 100,000 atoms at a very low computational cost.
We expect our ML model to set standards in a number of ways. Using our ML model either directly or in conjunction with other ML workflows, such as ML interatomic potentials for pre-sampling of atomic configurations, will enable first-principles modeling of materials without finite-size errors. Combined with Monte-Carlo sampling and atomic forces from automatic differentiation, our ML model can replace ML interatomic potentials and yield thermodynamic observables at much higher accuracy.
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