Quantum Monte Carlo (QMC) methods are some of the most accurate techniques available for calculating the electronic properties of molecules and materials, yet it often remains a challenge to economically compute forces using these techniques. As a result, quantum Monte Carlo methods are rarely employed to perform structural relaxations or <i>ab initio</i> molecular dynamics simulations. One potential approach for accelerating the computation of ``QMC forces'' is to machine learn these forces from QMC energy calculations. In this work, we employ Behler-Parrinello Neural Networks to learn QMC forces from Diffusion Monte Carlo calculations for geometry optimization and molecular dynamics simulations of small molecules. The task of learning QMC forces from Diffusion Monte Carlo simulations is uniquely challenging because of these simulations' stochastic nature and the fact that, unlike other electronic structure techniques that have been paired with machine learning, they do not readily provide force information for model training. Here, we illustrate that, despite these challenges, QMC can still be paired with machine learning to achieve promising results for small molecular systems, while clearly demonstrating the compromises in terms of the training set size and machine learning technique employed to make QMC geometry optimization and molecular dynamics possible. Our work provides a much-needed means of performing dynamics simulations on high-accuracy, QMC PESs and for generating QMC-quality molecular and materials structures.

Machine learning quantum monte carlo forces

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