Searching Configurations in Uncertainty Space: Active Learning of High-Dimensional Neural Network Reactive Potentials

Neural network (NN) potential energy surfaces (PESs) have been widely used in atomistic simulations with ab initio accuracy. While constructing NN PESs, their training data points are often sampled by molecular dynamics trajectories. This strategy can be however inefficient for reactive systems involving rare events. Here, we develop an uncertainty-driven active learning strategy to automatically and efficiently generate high-dimensional NN-based reactive potentials, taking a gas-surface reaction as an example. The difference between two independent NN models is used as a simple and differentiable uncertainty metric, allowing us to quickly search in the uncertainty space and place new samples at which the PES is less reliable. By interfacing this algorithm with the first-principles simulation package, we demonstrate that a globally accurate NN potential of the H₂ + Ag(111) system can be constructed with merely ∼150 data points. This PES can be further refined to describe H₂ dissociation on Ag(100) by adding ∼130 more configurations on this facet. The entire process is completely automatic and self-terminated once the relative error criterion is fulfilled. Impressively, data points sampled by this uncertainty-driven strategy are substantially fewer than by the traditional trajectory-based sampling. The final NN PES not only converges well the quantum dissociation probability of the molecule but also well-reproduces the phonon properties of the substrate and is capable of describing surface temperature effects. These results show the potential of this active learning approach in developing high-dimensional NN reactive potentials in gas and condensed phases.