Electronic Structure Prediction of Multi-million Atom Systems Through Uncertainty Quantification Enabled Transfer Learning

The ground state electron density - obtainable using Kohn-Sham Density Functional Theory (KS-DFT) simulations - contains a wealth of material information, making its prediction via machine learning (ML) models attractive. However, the computational expense of KS-DFT scales cubically with system size which tends to stymie training data generation, making it difficult to develop quantifiably accurate ML models that are applicable across many scales and system configurations. Here, we address these fundamental challenges using Bayesian neural networks and employ transfer learning to leverage the multi-scale nature of the training data. Our ML models employ descriptors involving simple scalar products, comprehensively sample system configurations through thermalization, and quantify uncertainty in electron density predictions. We show that our models incur significantly lower data generation costs while allowing confident - and when verifiable, accurate - predictions for a wide variety of bulk systems well beyond training, including systems with defects, different alloy compositions, and at unprecedented, multi-million-atom scales