Determination of melting and liquidlike–gaslike supercritical transition of 3D Yukawa systems from multi-head self-attention neural network

Following the neural network technology, both the supervised and unsupervised schemes are developed to identify the solid–fluid phase transition and the liquidlike–gaslike supercritical transition for three-dimensional (3D) Yukawa systems. The multi-head self-attention neural network (NN) models, named as the NNA and NNB models, are built for the supervised and unsupervised schemes, respectively. To obtain the dynamic and local structure data of individual particles for training these models, 150 independent molecular dynamics simulations of 3D Yukawa systems under various conditions are performed. After the training procedure of these models, the phases/states of 3D Yukawa systems under other conditions are effectively identified by the supervised scheme of the NNA models, purely from the information of individual particles. The solid–fluid transition and the liquidlike–gaslike supercritical transition points are also accurately obtained from these identified results from the NNA models. From the unsupervised scheme of the NNB model, in the complete absence of any artificial prior knowledge regarding the phase/state information, both the solid–fluid transition for 3D Yukawa systems and the transition between different lattice structures for 3D Yukawa solids are successfully identified, purely based on the underlying physics information in the dynamic and local structure data of individual particles.