Machine learning estimators for lattice QCD observables

A novel technique using machine learning (ML) to reduce the computational cost of evaluating lattice 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 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 $CP$ violating interaction, the quark chromoelectric dipole moment interaction, is added to QCD, again from the two-point correlation functions calculated without $CP$ violation.