Abstract
A novel technique using machine learning (ML) to reduce the computational cost of evaluating lattice quantum chromodynamics (QCD) observables is presented. The ML is trained on a subset of background gauge field configurations, called the labeled set, to predict an observable $O$ from the values of correlated, but less compute-intensive, observables $\mathbf{X}$ calculated on the full sample. By using a second subset, also part of the labeled set, we estimate the bias in the result predicted by the trained ML algorithm. A reduction in the computational cost by about $7\%-38\%$ is demonstrated for two different lattice QCD calculations using the Boosted decision tree regression ML algorithm: (1) prediction of the nucleon three-point correlation functions that yield isovector charges from the two-point correlation functions, and (2) prediction of the phase acquired by the neutron mass when a small Charge-Parity (CP) violating interaction, the quark chromoelectric dipole moment interaction, is added to QCD, again from the two-point correlation functions calculated without CP violation.
Highlights
Simulations of lattice QCD provide values of physical observables from correlation functions calculated as averages over gauge field configurations, which are generated using a Markov chain Monte Carlo method using the action as the Boltzmann weight [1,2]
We have proposed a Schwinger source method approach (SSM) [35,36] that exploits the fact that the chromoelectric dipole moment (cEDM) operator is a quark bilinear
The proposed machine learning (ML) algorithm used to predict compute-intensive observables from simpler measurements gives a modest computational cost reduction of 7%–38% depending on the observables analyzed here, as summarized in Tables IV (VP2) and V (P2)
Summary
Simulations of lattice QCD provide values of physical observables from correlation functions calculated as averages over gauge field configurations, which are generated using a Markov chain Monte Carlo method using the action as the Boltzmann weight [1,2]. We introduce a general ML method for estimating observables calculated using expensive Markov chain Monte Carlo simulations of lattice QCD that reduce the computational cost. Consider M samples of independent measurements of a set of observables Xi 1⁄4 fo1i ; o2i ; o3i ; ...g, i 1⁄4 1; ...; M, but the target observable Oi is available only on N of these These N are called the labeled data, and the remaining. We account for the full error, including the sampling variance of the training and the bias correction datasets, by using a bootstrap procedure [10] that independently selects N labeled and M − N unlabeled items for each bootstrap sample.
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