Latent space active learning with message passing neural network: The case of HfO 2

Due to their excellent abilities, machine learning potential models have shown significant promise in accurately constructing potential energy surfaces for various materials. As a data-driven approach, however, the training of these models necessitates carefully curated datasets to be effective. In this paper, we propose an active learning scheme for message passing neural networks (MPNNs). This method leverages the latent distance in the descriptor space, inherently generated by MPNNs, to quantify model uncertainty. Additionally, we employ CUR matrix decomposition for sample selection to reduce data redundancy. We demonstrate the application of this method on ${\mathrm{HfO}}₂$, a complex ferroelectric material with many phases, by investigating its static properties, phonon spectrum, and notably, structural phase transitions. We also demonstrate the reliability of latent distance as a model uncertainty metric. Utilizing latent space distance, the proposed method enriches active learning frameworks for machine learning potentials, providing an efficient alternative to traditional methods, such as the ``query by committee'' approach.