Epistemic uncertainty as a diagnostic probe for deep learning Hamiltonians

The reliability of deep learning models for Hamiltonian prediction remains poorly understood, limiting their deployment in computational materials discovery workflows. Although these models offer an efficient alternative to density functional theory (DFT), they are vulnerable to producing confident but incorrect predictions when applied beyond their training distribution. Here, we systematically quantify the applicability domain of Hamiltonian prediction models using ensemble variance as a built-in uncertainty metric. Using bilayer and twisted bilayer graphene as well-controlled testbeds, we demonstrate that ensemble variance (Δσ) exhibits strong linear correlation with mean absolute error (MAE) in all structural modulations (Pearson correlation coefficient >0.91), which allows it to serve as a DFT-free reliability indicator. The model maintains high accuracy (MAE < 2.5 meV) within limited structural perturbations: uniaxial strain from to 5%, interlayer distance from 2.95 to 3.75 Å, and length of the C-C bond from 1.41 to 1.44 Å. We further evaluated transfer to other carbon allotropes and obtained MAE values of 13.02 meV for graphite (Δσ = 3.93 meV), 13.99 meV for twisted graphite (Δσ = 3.94 meV), 15.80 meV for carbon nanotubes (Δσ = 4.09 meV), and 39.45 meV for fullerenes (Δσ = 10.85 meV). These results establish ensemble variance as a practical reliability indicator and underscore the critical need for pre-establishing applicability boundaries before deploying machine learning models in computational research workflows.