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. In this work, we discuss the development of a graph-based model for the approximation of one or more nucleation CVs, which 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 by 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. Further, we show that our approach is general and transferable to more complex CVs by learning CVs based on expensive SOAP descriptors for a copper melt and learning CVs for a system of flexible organic molecules.