Fig. 1: Schematic illustrations of carbon-growth-on-metal machine-learning potential (CGM-MLP) generated by active learning on-the-fly during hybrid molecular dynamics and time-stamped force-biased Monte Carlo (MD/tfMC) simulations.
a The initial training dataset includes representative carbon structures from Gaussian Approximation Potential (GAP-20)34 and C1-C18 carbon clusters on Cu(111) surfaces. b The CGM-MLP trained from this dataset is then used in a deposition simulation employing a hybrid MD/tfMC method27. c A smooth overlap of atomic positions (SOAP-based) algorithm is used to select the most representative structures from the MD/tfMC simulations. The inset figure presents the force correlation plots by using different quality control parameters, namely Nf (the number of structures sampled for each deposited carbon atom), Smax, and Save (i.e., the thresholds for the maximum and average SOAP distances, Dave and Dmax). The definitions of the similarity matrix Dave and Dmax are available in the “Methods” section. Source data and code are provided. d DFT benchmarks energy and force, and if the error is below a threshold, MD/tfMC continues. Otherwise, the training dataset is updated with newly selected structures.
