Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window

TL;DR

This paper demonstrates that neural networks trained on unphysical lattice configurations can accurately predict the deconfinement temperature in SU(2) and SU(3) gauge theories, acting as a numerical analog of analytical continuation.

Contribution

It introduces a machine learning approach that learns gauge-invariant functions at unphysical parameters to predict physical phase transition observables across parameter space.

Findings

Neural networks trained at unphysical parameters predict physical order parameters accurately.

The approach acts as a numerical analog of analytical continuation in lattice gauge theories.

Neural networks build gauge-invariant functions correlating with physical observables.

Abstract

We study the machine learning techniques applied to the lattice gauge theory's critical behavior, particularly to the confinement/deconfinement phase transition in the SU(2) and SU(3) gauge theories. We find that the neural network, trained on lattice configurations of gauge fields at an unphysical value of the lattice parameters as an input, builds up a gauge-invariant function, and finds correlations with the target observable that is valid in the physical region of the parameter space. In particular, if the algorithm aimed to predict the Polyakov loop as the deconfining order parameter, it builds a trace of the gauge group matrices along a closed loop in the time direction. As a result, the neural network, trained at one unphysical value of the lattice coupling $\beta$ predicts the order parameter in the whole region of the $\beta$ values with good precision. We thus demonstrate that the machine learning techniques may be used as a numerical analog of the analytical continuation from easily accessible but physically uninteresting regions of the coupling space to the interesting but potentially not accessible regions.