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.

Training algorithm matters for the performance of neural network potential: A case study of Adam and the Kalman filter optimizers.

One hidden yet important issue for developing neural network potentials (NNPs) is the choice of training algorithm. In this article, we compare the performance of two popular training algorithms, the adaptive moment estimation algorithm (Adam) and the extended Kalman filter algorithm (EKF), using the Behler-Parrinello neural network and two publicly accessible datasets of liquid water [Morawietz et al., Proc. Natl. Acad. Sci. U. S. A. 113, 8368-8373, (2016) and Cheng et al., Proc. Natl. Acad. Sci. U. S. A. 116, 1110-1115, (2019)]. This is achieved by implementing EKF in TensorFlow. It is found that NNPs trained with EKF are more transferable and less sensitive to the value of the learning rate, as compared to Adam. In both cases, error metrics of the validation set do not always serve as a good indicator for the actual performance of NNPs. Instead, we show that their performance correlates well with a Fisher information based similarity measure.