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The ground state electron density - obtainable using Kohn-Sham DensityFunctional Theory (KS-DFT) simulations - contains a wealth of materialinformation, making its prediction via machine learning (ML) models attractive.However, the computational expense of KS-DFT scales cubically with system sizewhich tends to stymie training data generation, making it difficult to developquantifiably accurate ML models that are applicable across many scales andsystem configurations. Here, we address this fundamental challenge by employingtransfer learning to leverage the multi-scale nature of the training data. OurML models employ descriptors involving simple scalar products, comprehensivelysample system configurations through thermalization, and quantify uncertaintyin electron density predictions using Bayesian neural networks. We show thatour models incur significantly lower data generation costs while allowingconfident - and when verifiable, accurate - predictions for a wide variety ofbulk systems well beyond training, including systems with defects, differentalloy compositions, and at unprecedented, multi-million-atom scales.

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