Error reduction using machine learning on Ising worm simulation

TL;DR

This paper introduces a machine learning approach to reduce statistical errors in higher moments measurements of the Ising model with an external field, enhancing the accuracy of simulation results.

Contribution

The study presents a novel machine learning method, specifically decision trees, to improve the estimation of higher moments in Ising worm simulations, compared to traditional measurement techniques.

Findings

Machine learning reduces statistical errors in higher moments.

Improved measurements align better with analytic predictions.

Method enhances accuracy of susceptibility and magnetization moments.

Abstract

We develop a method to improve on the statistical errors for higher moments using machine learning techniques. We present here results for the dual representation of the Ising model with an external field, derived via the high temperature expansion and simulated by the worm algorithm. We compare two ways of measuring the same set of observables, without and with machine learning: moments of the magnetization and the susceptibility can be improved by using the decision tree method to train the correlations between the higher moments and the second moment obtained from an integrated 2-point function. Those results are compared in small volumes to analytic predictions.