SemiH: DFT Hamiltonian neural network training with semi-supervised learning

Over the past decades, density functional theory (DFT) calculations have been utilized in various fields such as materials science and semiconductor devices. However, due to the inherent nature of DFT calculations, which rigorously consider interactions between atoms, they require significant computational cost. To address this, extensive research has recently focused on training neural networks to replace DFT calculations. However, previous methods for training neural networks necessitated an extensive number of DFT simulations to acquire the ground truth (Hamiltonians). Conversely, when dealing with a limited amount of training data, deep learning models often display increased errors in predicting Hamiltonians and band structures for testing data. This phenomenon poses the potential risk of generating inaccurate physical interpretations, including the emergence of unphysical branches within band structures. To tackle this challenge, we propose a novel deep learning-based method for calculating DFT Hamiltonians, specifically tailored to produce accurate results with limited training data. Our framework not only employs supervised learning with the calculated Hamiltonian but also generates pseudo Hamiltonians (targets for unlabeled data) and trains the neural networks on unlabeled data. Particularly, our approach, which leverages unlabeled data, is noteworthy as it marks the first attempt in the field of neural network Hamiltonians. Our framework showcases the superior performance of our framework compared to the state-of-the-art approach across various datasets, such as MoS2, Bi2Te3, HfO2, and InGaAs. Moreover, our framework demonstrates enhanced generalization performance by effectively utilizing unlabeled data, achieving noteworthy results when evaluated on data more complex than the training set, such as configurations with more atoms and temperature ranges outside the training data.