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

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 .