Machine Learning Forces Trained by Gaussian Process in Liquid States: Transferability to Temperature and Pressure

We study the generalization performance of a machine learning (ML) model to predict the atomic forces within density functional theory (DFT). The targets are Si and Ge single-component systems in the liquid state. To train the machine learning model, Gaussian process regression is performed with atomic fingerprints that express the local structure around the target atom. The training and test data are generated by molecular dynamics (MD) based on DFT. We first report the accuracy of ML forces when both test and training data are generated from the DFT-MD simulations at the same temperature. By comparing the accuracy of ML forces at various temperatures, it is found that the accuracy becomes the lowest around the phase boundary between the solid and liquid states. Furthermore, we investigate the transferability of ML models trained in the liquid state to temperature and pressure. We demonstrate that, if the training is performed at a high temperature and if the volume change is not so large, the transferability of ML forces in the liquid state is sufficiently high, whereas its transferability to the solid state is very low.