Training models using forces computed by stochastic electronic structure methods

TL;DR

This paper explores how stochastic electronic structure methods, particularly Quantum Monte Carlo, can be used to generate data for machine learning models of potential energy surfaces, highlighting advantages of stochastic noise in training.

Contribution

It demonstrates that stochastic errors from Quantum Monte Carlo can be beneficial for training machine learning models and provides analysis of their effects on model accuracy and error estimation.

Findings

Stochastic noise can improve model quality in certain cases.

Many imprecise data points can be advantageous for model construction.

Quantum Monte Carlo noise helps estimate model errors.

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.