Adaptive energy reference for machine-learning models of the electronic density of states

Machine learning methods for predicting electronic density of states often assume that the model predictions and targets share the same absolute energy reference. However, this overlooks a subtle point, that the absolute energy reference cannot be defined for infinite bulk systems due to the conditionally convergent nature of electrostatic potentials. This paper introduces a training framework that uses a self-aligning loss function to provide an adaptive energy reference during training. Models trained using this framework outperform those relying on fixed conventional internal energy references, like the Fermi level or average Hartree potential. The paper also sheds insights on how the adaptive reference enhances model performance and identifies the conditions under which they are the most effective.