Machine Learning-Based Estimation of Cumulants of Chiral Condensate via Multi-Ensemble Reweighting with Deborah.jl

TL;DR

This paper develops a bias-corrected machine learning method to efficiently estimate higher-order cumulants of the chiral condensate in finite-temperature QCD, reducing computational costs while maintaining accuracy.

Contribution

It introduces a novel bias correction approach for ML-based estimation of Dirac operator traces, enabling accurate higher cumulant calculations with less data and no explicit stochastic trace inputs.

Findings

ML estimates match baseline measurements within statistical errors.

Computational cost reduced to approximately 26%.

Bias correction enhances prediction stability in feature-only models.

Abstract

We investigate a bias-corrected machine learning (ML) strategy for estimating traces of the inverse Dirac operator, $\text{Tr}\, M^{-n}$ ($n=1,2,3,4$), motivated by the need for higher-order cumulants of the chiral condensate near the finite-temperature QCD critical endpoint. Our supervised regression framework is trained on Wilson-clover ensembles with the Iwasaki gauge action, and we explore two input feature scenarios: one using $\text{Tr}\, M^{-1}$ and another relying solely on gauge observables (plaquette and rectangle), enabling a fully feature-based prediction pipeline. Using $\text{Tr}\, M^{-1}$ both as a physical input to cumulant construction and as a feature for predicting higher powers, we find that even with $\sim1\%$ labeled data, the resulting susceptibility, skewness, and kurtosis remain statistically consistent with fully measured baselines, reducing computational cost to about $26\%$. In the feature-only approach, where correlations rather than explicit stochastic traces drive the predictions, bias correction plays a more pronounced role. We quantify this impact through multi ensemble reweighting across nearby quark masses. Our results demonstrate that bias-corrected ML estimates can significantly reduce measurement overhead while preserving the stability of higher-order observables relevant for locating the QCD critical endpoint. Code for this work is available at https://github.com/saintbenjamin/Deborah.jl .