Extracting critical exponents by finite-size scaling with convolutional neural networks

Machine learning has been successfully applied to identify phases and phase transitions in condensed matter systems. However, quantitative characterization of the critical fluctuations near phase transitions is lacking. In this study we extract the critical behavior of a quantum Hall plateau transition with a convolutional neural network. We introduce a finite-size scaling approach and show that the localization length critical exponent learned by the neural network is consistent with the value obtained by conventional approaches. We illustrate the physics behind the approach by a cross-examination of the inverse participation ratios.