Training models using forces computed by stochastic electronic structure methods

Abstract

Quantum Monte Carlo (QMC) can play a very important role in generating accurate data needed for constructing potential energy surfaces. We argue that QMC has advantages in terms of a smaller systematic bias and an ability to cover phase space more completely. The stochastic noise can ease the training of the machine learning model. We discuss how stochastic errors affect the generation of effective models by analyzing the errors within a linear least squares procedure, finding that there is an advantage to having many relatively imprecise data points for constructing models. We then analyze the effect of noise on a model of many-body silicon finding that noise in some situations improves the resulting model. We then study the effect of QMC noise on two machine learning models of dense hydrogen used in a recent study of its phase diagram. The noise enable us to estimate the errors in the model. We conclude with a discussion of future research problems.

References in corpus (3)

• The Finite Size Error in Many-body Simulations with long-Ranged Interactions
• Accurate, efficient and simple forces with Quantum Monte Carlo methods
• Trial wave functions for High-Pressure Metallic Hydrogen

Cited by in corpus (5)

• First principles simulations of dense hydrogen
• Accurate quantum Monte Carlo forces for machine-learned force fields: Ethanol as a benchmark
• Efficient calculation of unbiased atomic forces in ab initio Variational Monte Carlo
• Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer
• Fast Evaluation of Unbiased Atomic Forces in ab initio Variational Monte Carlo via the Lagrangian Technique