Testing machine-learned distributions against Monte Carlo data for the QCD chiral phase transition

TL;DR

This paper introduces a flexible machine learning approach using conditional Masked Autoregressive Flows to interpolate lattice QCD observables across parameters, reducing computational costs in studying the QCD chiral phase transition.

Contribution

It demonstrates the effectiveness of this method in interpolating in parameters where traditional reweighting is difficult, enabling rapid sampling and initial phase boundary estimates.

Findings

Successfully reproduces reweighting in gauge coupling

Extends interpolation to quark mass and volume

Generates samples in minutes for full parameter space

Abstract

We demonstrate that conditional Masked Autoregressive Flows constitute a flexible interpolation tool for lattice QCD observables, conditioned on bare lattice parameters. As a benchmark, we use the chiral phase structure of QCD with five degenerate light quark flavours, which on coarse lattices exhibits a region of first-order chiral transitions terminating in a critical quark mass. The method successfully reproduces standard reweighting in the gauge coupling, and naturally extends to interpolation in quark mass and spatial volume, for which reweighting is computationally prohibitive or inapplicable, respectively. Once trained, the model generates samples across the full parameter space in minutes, which can be used to obtain consistent first estimates of the critical quark mass without simulating all intermediate parameter values. This offers a concrete reduction in the number of lattice ensembles required. Precision on the critical mass from learned distributions is so far prohibited by the mode-covering effect inherent to maximum-likelihood-based training, which introduces a systematic bias near first-order transitions. At the current stage, the method is well-suited for a range of practical applications: localising phase boundaries, identifying the universal scaling axes at a critical point, and accelerating informed determinations of parameter values ahead of high-precision Monte Carlo campaigns.