Machine learning estimators for lattice QCD observables

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 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. The bias-corrected final estimate of the expectation value of O, obtained by running the ML algorithm on the remaining unlabeled set, is improved by combining with the labeled data. A reduction in the computational cost by about 35% is demonstrated for two different lattice QCD calculations using the Boosted decision tree (BDT) 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 chromo-electric dipole moment interaction, is added to QCD, again from the two-point correlation functions calculated without CP violation.PACS numbers: 11.15. Ha, 12.38.Gc 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]. Each measurement is computationally expensive and a standard technique to reduce the cost is to replace the 'high precision' (HP) average of an observable O by a 'low precision' (LP) version of it, O LP [3,4], and then perform bias correction (BC), i.e., O = O LP + O − O LP . The method works because the second term can be estimated with sufficient precision from a smaller number of measurements if the covariance between O and O LP is positive and comparable to the variance of O, which is the case if, for example, the fluctuations in either is controlled by effects common to both. One can replace O LP in the above formulation with any quantity whose statistical fluctuations are similar to that of O. Since most underlying gauge dynamics affect a plethora of observables in a similar way, such quantities surely exist; the trick, however, is to find suitable sets of quantities.Machine learning algorithms (ML) build predictive models from data. In contrast to conventional curvefitting techniques, ML does not use "few parameter functional family" of forms for the prediction. Instead, it searches over the entire space of functions approximated using a general form with a large number of free parameters that require a correspondingly large amount of training data to avoid overfitting. ML has been successful for various applications where such data are available, including exotic particle searches [5] and Higgs → τ τ analyses [6] at the Large Hadron Collider. It has recently been applied to ...

Machine-learning prediction for quasiparton distribution function matrix elements

“…We follow the bias-correction strategy introduced in Ref. [25] to remove the bias in our estimate and define the bias-corrected prediction as…”

“…Each subset of the data (training, bias-correction, and unlabeled datasets) described in Ref. [25] are chosen such that the configurations are evenly distributed. The convention of notations throughout this work is given in Table I.…”

“…Recently, authors of Ref. [25] introduced a machinelearning (ML) approach predicting observables by taking advantage of the correlations between lattice-QCD observables. Two types of data with high-statistics measurements, Oð100; 000Þ, were used in the studies: nucleon isovector charges and the CP-violating phase induced by the quark chromoelectric dipole moment interactions.…”

Flavor-diagonal CP violation: the electric dipole moment

“…The second aspect to mention is the use of Machine Learning (ML) algorithms [ 148 ] in the evaluation of lattice correlators. The intent is to “learn” the relation between observables of different computational costs and which are correlated.…”

Status and future perspectives for lattice gauge theory calculations to the exascale and beyond

“…A number of ML approaches well suited to this task have been applied successfully to similar problems in molecular design and drug discovery. Recently, an ML approach to determining estimators for lattice QCD has also been explored [132].…”