Capturing the universality class of the 2D ising model via symmetry-corrected machine learning and finite-size scaling

Machine learning (ML) has emerged as a powerful tool for identifying phase transitions, yet ensuring that ML models capture the underlying physical laws rather than merely memorizing data patterns remains a challenge. In this study, we present a robust, symmetry-corrected ML pipeline to determine the critical temperature Tc and the universality class of the two-dimensional Ising model. By implementing a gauge-fixing preprocessing step to restore broken symmetry and utilizing Principal Component Analysis (PCA) coupled with Logistic Regression, we analyze a massive dataset spanning lattice sizes from L=32 to L=96. Our approach integrates classical Finite-Size Scaling (FSS) theory directly into the ML analysis. We demonstrate that the ML-predicted ferromagnetic probabilities exhibit a high-quality data collapse when scaled with the exact critical exponent ν=1, providing strong evidence that the model successfully learns the order parameter fluctuations. Quantitatively, our method achieves a critical temperature prediction of Tc≈2.27178 for L=96, which deviates by only ∼0.6\% from the exact Onsager solution. Furthermore, we employ a non-parametric bootstrap method to provide rigorous uncertainty quantification. This work establishes a transparent and reproducible framework for applying ML to statistical physics problems, demonstrating that symmetry-aware preprocessing is essential for high-precision critical point estimation.