Atomistic learning in the electronically grand-canonical ensemble

A strategy is presented for the machine-learning emulation of electronic structure calculations carried out in the electronically grand-canonical ensemble.The approach relies upon a dual-learning scheme,where both the system charge and the system energy are predicted for each image.The scheme is shown to be capable of emulating basic electrochemical reactions at a range of potentials,and coupling it with a bootstrap-ensemble approach gives reasonable estimates of the prediction uncertainty.The method is also demonstrated to accelerate saddle-point searches,and to extrapolate to systems with one to five water layers.We anticipate that this method will allow for larger length-and time-scale simulations necessary for electrochemical simulations.