Machine Learning Estimation on the Trace of Inverse Dirac Operator using the Gradient Boosting Decision Tree Regression

TL;DR

This paper explores using gradient boosting decision trees to efficiently estimate the trace of the inverse Dirac operator, aiming to reduce computational costs compared to traditional linear solvers.

Contribution

It introduces a machine learning approach for trace estimation of the inverse Dirac operator, offering a potentially faster alternative to conventional methods.

Findings

Gradient boosting decision trees can estimate traces with reduced computational effort.

Bias effects in the estimation are identified and discussed.

Preliminary results show promise for machine learning in lattice QCD computations.

Abstract

We present our preliminary results on the machine learning estimation of $\text{Tr} \, M^{-n}$ from other observables with the gradient boosting decision tree regression, where $M$ is the Dirac operator. Ordinarily, $\text{Tr} \, M^{-n}$ is obtained by linear CG solver for stochastic sources which needs considerable computational cost. Hence, we explore the possibility of cost reduction on the trace estimation by the adoption of gradient boosting decision tree algorithm. We also discuss effects of bias and its correction.