Machine Learning Diffusion Monte Carlo Energies

TL;DR

This paper introduces two machine learning methods, VDNNs and KRR, to accurately predict diffusion Monte Carlo energies across various materials using small datasets, outperforming traditional approaches.

Contribution

The study demonstrates that kernel ridge regression and voxel deep neural networks can predict DMC energies with high accuracy, even for complex systems, using minimal training data.

Findings

KRR outperforms VDNNs and other ML models on pristine graphene.

KRR achieves chemical accuracy in energy barrier predictions for defects.

KRR accurately predicts total energies of liquid water in 3D materials.

Abstract

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.