Self-learning Hybrid Monte Carlo: A First-principles Approach

TL;DR

The paper introduces Self-Learning Hybrid Monte Carlo (SLHMC), a method combining machine learning potentials with first-principles DFT simulations to accelerate sampling while maintaining accuracy, and adaptively improving the ML potential during simulations.

Contribution

SLHMC is a novel approach that integrates machine learning potentials with DFT to enable efficient, exact sampling and on-the-fly potential optimization.

Findings

SLHMC achieves efficient sampling in complex materials.

The ANN potential attains meV/atom accuracy.

The method is transferable to molecular dynamics simulations.

Abstract

We propose a novel approach called Self-Learning Hybrid Monte Carlo (SLHMC) which is a general method to make use of machine learning potentials to accelerate the statistical sampling of first-principles density-functional-theory (DFT) simulations. The trajectories are generated on an approximate machine learning (ML) potential energy surface. The trajectories are then accepted or rejected by the Metropolis algorithm based on DFT energies. In this way the statistical ensemble is sampled exactly at the DFT level for a given thermodynamic condition. Meanwhile the ML potential is improved on the fly by training to enhance the sampling, whereby the training data set, which is sampled from the exact ensemble, is created automatically. Using the examples of $\alpha$-quartz crystal SiO$_2^{}$ and phonon-mediated unconventional superconductor YNi$_2^{}$B$_2^{}$C systems, we show that SLHMC with artificial neural networks (ANN) is capable of very efficient sampling, while at the same time enabling the optimization of the ANN potential to within meV/atom accuracy. The ANN potential thus obtained is transferable to ANN molecular dynamics simulations to explore dynamics as well as thermodynamics. This makes the SLHMC approach widely applicable for studies on materials in physics and chemistry.