A recipe for cracking the quantum scaling limit with machine learned electron densities

A long-standing goal of science is to accurately simulate large molecular systems using quantum mechanics. The poor scaling of current quantum chemistry algorithms on classical computers, however, imposes an effective limit of about a few dozen atoms on traditional electronic structure calculations. We present a machine learning (ML) method to break through this scaling limit for electron densities. We show that Euclidean neural networks can be trained to predict molecular electron densities from limited data. By learning the electron density, the model can be trained on small systems and make accurate predictions on large ones. In the context of water clusters, we show that an ML model trained on clusters of just 12 molecules contains all the information needed to make accurate electron density predictions on cluster sizes of 50 or more, beyond the scaling limit of current quantum chemistry methods.