Machine Learning Nucleation Collective Variables with Graph Neural Networks

The efficient calculation of nucleation collective variables (CVs) is one of the main limitations to the ap- plication of enhanced sampling methods to the investigation of nucleation processes in realistic environments. Here we discuss the development of a graph-based model for the approximation of nucleation CVs, which en- ables orders-of-magnitude gains in computational efficiency in the on-the-fly evaluation of nucleation CVs. By performing simulations on a nucleating colloidal system, we assess the model’s efficiency in both postprocessing and on-the-fly biasing of nucleation trajectories, thereby mimicking a multistep nucleation process from solu- tion. Moreover, we probe and discuss the transferability of the graph model approximations across systems by using the model of a CV based on sixth-order Steinhardt parameters. The model was trained with data collected from a colloidal system and was used to drive the nucleation of crystalline copper from its melt. Our approach is general and fully transferable to more complex systems as well as to different CVs.