Machine Learning for Dynamic Critical Exponent Estimation in the Three-Dimensional Ising Model with Limited Computational Resources

The dynamic critical exponent z describes the divergence of correlation times near a continuous phase transition. Obtaining accurate estimates of z from noisy time series is complex, especially when computational resources are limited. We compare machine learning approaches for estimating z in the three-dimensional Ising model. Data are generated from Monte Carlo simulations on a standard laptop computer, requiring 15 to 20 min of runtime. Twelve time-series features are extracted from the simulation output. We compare linear regression, simple scaling, and ensemble methods. Linear regression achieves a root mean square error of 0.0164 on the validation set with a coefficient of determination R2=0.974. The integrated autocorrelation time logτ shows a near-perfect correlation with z (the correlation value r=0.992), consistent with the system linear size scaling relation τ∼Lz. Autocorrelation features at three lags considered show correlations with z between 0.72 and 0.87. Standardised coefficient analysis indicates that the standard deviation of successive differences and the standard deviation of magnetisation are the dominant predictors in the standardised model, with coefficients of −0.246 and 0.239, respectively. Accurate exponent estimation is possible with minimal computational resources, and fluctuation-based features capture critical slowing down effectively.