Multifidelity Statistical Machine Learning for Molecular Crystal Structure Prediction

The prediction of crystal structures from first-principles requires highly accurate energies for large numbers of putative crystal structures. High accuracy of solid state density functional theory (DFT) calculations is often required, but hundreds or more structures can be present in the low energy region of interest, so that the associated computational costs are prohibitive. Here, we apply statistical machine learning to predict expensive hybrid functional DFT (PBE0) calculations using a multifidelity approach to re-evaluate the energies of crystal structures predicted with an inexpensive force field. The method uses an autoregressive Gaussian process, making use of less expensive GGA DFT (PBE) calculations to bridge the gap between the force field and PBE0 energies. The method is benchmarked on the crystal structure landscapes of three small, hydrogen-bonded organic molecules and shown to produce accurate predictions of energies and crystal structure ranking using small numbers of the most expensive calculations; the PBE0 energies can be predicted with errors of less than 1 kJ mol^-1 with between 4.2 and 6.8% of the cost of the full calculations. As the model that we have developed is probabilistic, we discuss how the uncertainties in predicted energies impact the assessment of the energetic ranking of crystal structures.