Applying machine learning methods to prediction problems of lattice observables

TL;DR

This paper demonstrates that neural networks can predict critical behavior of lattice gauge observables, learning gauge-invariant correlations even outside their training region, offering a new approach to analyzing gauge theories.

Contribution

It introduces a neural network method that predicts lattice observable behavior and confirms gauge invariance without prior explicit encoding of gauge symmetry.

Findings

Neural networks successfully predict critical behavior of lattice observables.

The network constructs gauge-invariant functions across parameter space.

Prediction remains accurate even outside the training region.

Abstract

We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge theories. We show that feed-forward neural network, trained on the lattice configurations of gauge fields as input data, finds correlations with the target observable, which is also true in the critical region where the neural network has not been trained. We have verified that the neural network constructs a gauge-invariant function and this property does not change over the entire range of the parameter space.