  We present two machine learning methodologies that are capable of predicting
diffusion Monte Carlo (DMC) energies with small datasets (~60 DMC calculations
in total). The first uses voxel deep neural networks (VDNNs) to predict DMC
energy densities using Kohn-Sham density functional theory (DFT) electron
densities as input. The second uses kernel ridge regression (KRR) to predict
atomic contributions to the DMC total energy using atomic environment vectors
as input (we used atom centred symmetry functions, atomic environment vectors
from the ANI models, and smooth overlap of atomic positions). We first compare
the methodologies on pristine graphene lattices, where we find the KRR
methodology performs best in comparison to gradient boosted decision trees,
random forest, gaussian process regression, and multilayer perceptrons. In
addition, KRR outperforms VDNNs by an order of magnitude. Afterwards, we study
the generalizability of KRR to predict the energy barrier associated with a
Stone-Wales defect. Lastly, we move from 2D to 3D materials and use KRR to
predict total energies of liquid water. In all cases, we find that the KRR
models are more accurate than Kohn-Sham DFT and all mean absolute errors are
less than chemical accuracy.
