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 application 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 that enables orders-of-magnitude gains in computational efficiency in the on-the-fly evaluation of nucleation CVs. By performing simulations on a nucleating colloidal system mimicking a multistep nucleation process from solution, we assess the model's efficiency in both postprocessing and on-the-fly biasing of nucleation trajectories with pulling, umbrella sampling, and metadynamics simulations. Moreover, we probe and discuss the transferability of graph-based models of nucleation CVs across systems using the model of a CV based on sixth-order Steinhardt parameters trained on a colloidal system to drive the nucleation of crystalline copper from its melt. Our approach is general and potentially transferable to more complex systems as well as to different CVs.