Physically informed neural network potential for a multi-element system

Various machine-learning potentials have been proposed for deeper understanding of complex concerted phenomena that involve too many atoms and molecules to be analyzed by first-principles electronic states calculations. However, the learning processes are purely mathematical, making their transferability to unknown structures problematic in some cases. Recently, the physically informed (PI) neural network (NN) potential has been proposed to resolve this issue. This approach uses well-known interatomic potential functions based on physical intuition, similar to an empirical potential with a few parameters, and the parameter sets are predicted by NN instead of predicting the function values, which improves the transferability. However, creating PINN potentials of multi-element systems is difficult because the appropriate parameter sets are difficult to know in advance. In the present study, we present a method to create the PINN potentials of a LiNiO 2 bulk crystal as a multi-element system. LiNiO 2 is considered to be formed mainly by the attractive interactions between Li and O atoms and those between O and Ni atoms; the other interactions are considered to be small. The resulting PINN potentials well reproduced such behaviors. As an application of the developed PINN potentials, we performed path integral molecular dynamics simulations. We found that the simulations operated stably enough to evaluate the radial distribution function for each element pair, and that the nuclear quantum effects became more pronounced as the elements became lighter.