  Predicting the mean-field Hamiltonian matrix in density functional theory is
a fundamental formulation to leverage machine learning for solving molecular
science problems. Yet, its applicability is limited by insufficient labeled
data for training. In this work, we highlight that Hamiltonian prediction
possesses a self-consistency principle, based on which we propose
self-consistency training, an exact training method that does not require
labeled data. It distinguishes the task from predicting other molecular
properties by the following benefits: (1) it enables the model to be trained on
a large amount of unlabeled data, hence addresses the data scarcity challenge
and enhances generalization; (2) it is more efficient than running DFT to
generate labels for supervised training, since it amortizes DFT calculation
over a set of queries. We empirically demonstrate the better generalization in
data-scarce and out-of-distribution scenarios, and the better efficiency over
DFT labeling. These benefits push forward the applicability of Hamiltonian
prediction to an ever-larger scale.
