Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window
This work addresses the challenge of accessing physically interesting regions in lattice gauge theories for researchers in theoretical physics, though it is incremental as it applies existing machine learning techniques to a new context.
The study tackled the problem of predicting the deconfinement temperature in lattice Yang-Mills theories by training a neural network on unphysical lattice configurations, and it achieved good precision in predicting the order parameter across the entire parameter space.
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 $β$ predicts the order parameter in the whole region of the $β$ 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.